What is Nirodha?

To add to both @Unrul3r @Andrei Volkov's answers.

You can break the links of Dependent Origination when you understand it at the experiential level. When enter the Attainment of Cessation you see the links in one direction (contact has ceased followed by ... ) and when coming out the other direction (contact has started followed by ... ). Depending on the clarity you achieve you enter one of the stages of sainthood.

Understanding of Path Leading Out of Misery and Path of Misery starts at with contact followed by sensation at the experiential level. This becomes clear and the understanding becomes 1st hand when you enter the Attainment of Cessation.

https://www.wisdomlib.org/definition/nirodha

Theravada (major branch of Buddhism)

Cessation; disbanding; stopping. (Source): Access to Insight: A Glossary of Pali and Buddhist Terms (Cessation) nirodha is the cessation of all aggregates and consciousness as a whole - even at a subtle level. In order to be experienced, it does require some specific determinations and the development of considerably more concentration than the one required for experiencing nibbana.

(Source): Dhamma Dana: Pali English Glossary s. Nirodha (“extinction”); - of craving: tanhakkhaya.

(Source): Pali Kanon: Manual of Buddhist Terms and Doctrines 'extinction'; s. nirodha-samāpatti, anupubba-nirodha.

(Source): Pali Kanon: Manual of Buddhist Terms and Doctrines context information

The word "nirodha" is used in similar contexts to the word "atthaṅgamañca". The words "origin" ("samudaya") and "passing away" {"atthaṅgama") appear defined in SN 22.5, as follows:

And what, bhikkhus, is the origin of form? What is the origin of feeling? What is the origin of perception? What is the origin of volitional formations? What is the origin of consciousness? Here, bhikkhus, one seeks delight, one welcomes, one remains holding. And what is it that one seeks delight in, what does one welcome, to what does one remain holding? One seeks delight in form, welcomes it, and remains holding to it. As a consequence of this, delight arises. Delight in form is clinging. With one’s clinging as condition, existence comes to be; with existence as condition, birth; with birth as condition, aging-and-death, sorrow, lamentation, pain, displeasure, and despair come to be. Such is the origin of this whole mass of suffering.

And what, bhikkhus, is the passing away of form? What is the passing away of feeling? What is the passing away of perception? What is the passing away of volitional formations? What is the passing away of consciousness? Here, bhikkhus, one does not seek delight, one does not welcome, one does not remain holding. And what is it that one does not seek delight in? What doesn’t one welcome? To what doesn’t one remain holding? One does not seek delight in form, does not welcome it, does not remain holding to it. As a consequence of this, delight in form ceases. With the cessation of delight comes cessation of clinging; with cessation of clinging, cessation of existence…. Such is the cessation of this whole mass of suffering.

Nirodha is the cessation of feeling and perceptions. The first Nirodha people will experience is when they first realized the way, in a split second everything stops and they will see the links of dependent origination. This will happen again every Magga and Phala. Once they realized and saw the way, they'll be able to get into Nirodha through Nirodha Samāpatti.

Meditation through SamathaVipassana will help you get into that. Jhana 1 - 4 all the way to base of neither perception nor non perception.

Then cut all of the Tanhas, until you feel Disenchanted and Dispassionate with the task and keep on cutting the Tanhas on the background until everything Ceased[Nirodha].

Only the Anagami that is able to get into NirodhaSamapatti anytime they want.

Hopefully this helps.

Extract from -
The Teaching of No Person: Only Dhātus
by Ajahn Buddhadāsa
Interpreted into English by Santikaro Bhikkhu
A Dhamma talk given at Suan Mokkh on 4 August 1991

So we can say that there is this body or form which is a dhātu (sankhara) – rūpa-dhātu (the form element). The mind then, is just another dhātu, the dhātu which experiences, feels, and thinks. This we can call the citta-dhātu (the mind element). Then there are the things which the mind thinks, feels, experiences – all these things connected with and associated with the mind are called the cetasika-dhātu. So in this life there are these three dhātus – the form dhātu, the mind dhātu, and the mental factors dhātu. This way of speaking has not been done before, we haven't come across others saying this, but to say that life is made up of these three dhātus is totally in line with nature and so we are free to say it. It is completely true that life is made of these three dhātus.

There is one more very special dhātu called the asaṅkhata-dhātu or the nibbāna-dhātu. This is the dhātu which is the quenching point when all other dhātus cease. All the saṅkhata-dhātus just mentioned are quenched in the nibbāna-dhātu. This kind of dhātu is much different than the ordinary dhātus because it's here where all other elements are quenched or extinguished.
When one dhātu gives way to another dhātu, there's one dhātu and then there's another dhātu, for this to happen depends on the element of cessation, for there's one dhātu which must cease for the next dhātu to appear. This dhātu which is the cessation of the ordinary dhātus is called nirodha-dhātu (the element of cessation). This isn't the same as the nibbāna-dhātu where the saṅkhata-dhātus are quenched thoroughly, but rather this is a temporary quenching or cessation, and so we call it nirodha-dhātu. So all the saṅkhatadhātus – mental, physical, and what have you – are quenched or ceased in this nirodha-dhātu. It's only because of this cessation element, that there is any possibility for change or evolution. If there wasn't this cessation element nothing could change, but this dhātu must cease for another dhātu to arise. The transformation from this dhātu into that dhātu only happens because of the nirodha-dhātu (the element of cessation). So all the saṅkhata-dhātus, or all changes, all worldly life depends on not only the saṅkhata-dhātus but this asaṅkhata-dhātu (the element of cessation).

I think it's originally from the Visuddhimagga

It's used before that, e.g. in the first sutta, it's in the definition of the third noble truth:

Idaṃ kho pana, bhikkhave, dukkha·nirodhaṃ ariya·saccaṃ: yo tassā·y·eva taṇhāya asesa·virāga·nirodho cāgo paṭinissaggo mutti anālayo.

Furthermore, bhikkhus, this is the dukkha·nirodha ariya·sacca: the complete virāga, nirodha, abandoning, forsaking, emancipation and freedom from that very taṇhā.

The Glossary says

nirodha: cessation. Used in many cases as a synonym of Nibānna.

On pages 38-39 (pages 12-13 of the PDF) of Piya Tan's introduction to this sutta, he writes,

The terms samudaya and nirodha are commonly tr respectively as “origin” and “ending, cessation.” However, from the teachings of this Sutta, which underlies the Buddha’s Teaching as a whole, they are better rendered as “arising” and “non-arising.” Payutto makes an important note:

Generally speaking, the word ‘cease’ [or ‘end’] means to do away with something which has already arisen, or the stopping of something which has already begun. However, nirodha in the teaching of Dependent Origination (as also in dukkhanirodha, the third of the noble truths) means non-arising, or non-existence, of something because the cause of its arising is done away with. For example, the phrase ‘when avijjā is nirodha, sakhārā are also nirodha,’ which is usually taken to mean, “with the cessation of ignorance, volitional impulse ceases,” in fact means that ‘when there is no ignorance, or no arising of ignorance, or when there is no longer any problem with ignorance, there is no volitional impulses, volitional impulses do not arise, or there is no longer any problem from volitional impulses.’ It does not mean that ignorance already arisen must be done away with before the volitional impulses which have already arisen will also be done away.

etc.

I tried to understand what it might mean etymologically; all I can offer on that is this discussion, perhaps especially this answer.

However Payutto (quoted by Piya Tan above) goes on to say,

Where nirodha should be rendered as cessation is when it is used in reference to the natural way of things, or the nature of compounded things. In this sense it is a synonym for the words bhaga (breaking up), anicca (transient), khaya (cessation) or vaya (decay). For example, in the Pali it is given: imaṁ kho bhikkhave tisso vedanā anicccā sakhatā paiccasamuppannā khayadhammā vayadhammā virāgadhammā nirodhadhammā—“Bhikshus, these three kinds of feelings are naturally impermanent, compounded, dependently arisen, transient, subject to decay, dissolution, fading and cessation” [S 4:214]. (All factors occurring in the Dependent Origination cycle have the same nature.) In this instance, the meaning is “all conditioned things (sakhāra), having arisen, must inevitably decay and fade according to supporting factors.” There is no need [here] to try to stop them, they cease of themselves.

As for nirodha in the third noble truth (or the Dependent Origination cycle in cessation mode), although it also describes a natural process, its emphasis is on practical considerations. It is translated in two ways in the Visuddhimagga [Vism 16.18/495]. One way traces the etymology to ni (without) + rodha (prison, confine[s], obstacle, wall, impediment), thus rendering the meaning as “without impediment,” “free from confinement.” This is explained as “free of impediments, that is, the confinement of saṁsāra.” Another definition traces the origin to anuppāda, meaning “not arising,” [and goes on to say “nirodha here does not mean bhaga, breaking up and dissolution.”]72

In summary it's understood to mean "cessation" ... and/or "non-arising", when the cause of arising ceases or doesn't arise or fades away or is abandoned etc. ... and/or Payutto (or the etymology)introduces a third possible meaning, i.e. "without obstacle", "liberation".

Given the etymology I find it difficult to see how it might mean "cessation" at all, rather than freedom; but the English translation of the Visuddhimagga explains that pretty well, saying,

The word ni denotes absence, and the word rodha a prison. Now, the third truth is void of all destinies (by rebirth) and so there is no constraint (rodha) of suffering here reckoned as the prison of the rounds of rebirth; or when cessation has been arrived at then there is no more constraint of suffering reckoned as the prison of the rounds of rebirth. And being the opposite of that prison, it is called dukkha-nirodha (cessation of suffering). Or alternatively it is called "cessation of suffering" because it is a condition for the cessation of suffering consisting in non-arising.

Daniel Goleman was mistaken. An excellent internet review of his book states:

Two notable mistakes are made in this section, one being the consistent misspelling of pañña as puñña (I get a little worried when an author misspells key terms), the second being the placement of nirodha-samapatti (“cessation of feeling and perception”) as above, or superior to, nibbana. There is no justification for this given the evidence of the Pali Suttas, where nirodha-samapatti is described rather as a kind of “super jhana” attainable only by anagamis and arhats. It is not, in itself, liberative.

In Buddhism, the key or essential meaning of 'nirodha' is in the same context of the 3rd noble truth & dependent origination. Here, it refers to the 'cessation of suffering' & the cessation of mental defilements that cause suffering (rather than 'cessation' per se).

The etymology of the word can certainly be examined however this may not satify every use of the word in the suttas.

It is best to examine context in the suttas, such as the Upaya Sutta, Iti 44 or MN 38:

Bhikkhus, if a bhikkhu has abandoned lust for the form element, with the abandoning of lust the basis is cut off: there is no support for the establishing of consciousness. If he has abandoned lust for the feeling element … for the perception element … for the volitional formations element … for the consciousness element, with the abandoning of lust the basis is cut off: there is no support for the establishing of consciousness.

When that consciousness is unestablished, not coming to growth, nongenerative, it is liberated. By being liberated, it is steady; by being steady, it is content; by being content, he is not agitated. Being unagitated, he personally attains Nibbāna.

Upaya Sutta

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What, bhikkhus, is the Nibbāna-element with residue left? Here a bhikkhu is an arahant, one whose taints are destroyed, the holy life fulfilled, who has done what had to be done, laid down the burden, attained the goal, destroyed the fetters of being, completely released through final knowledge. However, his five sense faculties remain unimpaired, by which he still experiences what is agreeable and disagreeable and feels pleasure and pain. It is the extinction of attachment, hate, and delusion in him that is called the Nibbāna-element with residue left.

Iti 44

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On seeing a form with the eye, he does not lust after it if it is pleasing; he does not dislike it if it is unpleasing. He abides with mindfulness of the body established, with an immeasurable mind, and he understands as it actually is the deliverance of mind and deliverance by wisdom wherein those evil unwholesome states cease without remainder. Having thus abandoned favouring and opposing, whatever feeling he feels, whether pleasant or painful or neither-painful-nor-pleasant, he does not delight in that feeling, welcome it, or remain holding to it. As he does not do so, delight in feelings ceases in him. With the cessation of his delight comes cessation of clinging; with the cessation of clinging, cessation of being; with the cessation of being, cessation of birth; with the cessation of birth, ageing and death, sorrow, lamentation, pain, grief, and despair cease. Such is the cessation of this whole mass of suffering.

MN 38

The above quotes show, in the context of Dependent Origination, the process of 'nirodha' is always about the extinguishing or cessation of the fires of the mental defilements (rather than the cessation or destruction of the aggregates, such as consciousness).

I directly knew as it actually is: ‘This is suffering’; I directly knew as it actually is: ‘This is the origin of suffering’; I directly knew as it actually is: ‘This is the cessation of suffering’; I directly knew as it actually is: ‘This is the way leading to the cessation of suffering.’ I directly knew as it actually is: ‘These are the taints’; I directly knew as it actually is: ‘This is the origin of the taints’; I directly knew as it actually is: ‘This is the cessation of the taints’; I directly knew as it actually is: ‘This is the way leading to the cessation of the taints.’

MN 4

In conclusion, 'nirodha', while sort of synonymous with 'Nibbana', always occurs before Nibbana thus is never above Nibbana.

When the mental defilements (of greed, hatred & ignorance) nirodha/extinguish (like a fire extinguishes), what remains is the peace or coolness of Nibbana & liberation of mind (ceto vimutti).

Thus, nirodha is the process of cessation of mental defilements and Nibbana is what remains.

For example, the term 'nirodha' is always used with the 'arising & ceasing' of defilements. In other words, 'nirodha' is the opposite of 'samudhaya' ('arising'). While the term 'Nibbana' is always used with the utter absence of defilements.

It is the extinction/destruction (khayo) of attachment, hate, and delusion in him that is called the Nibbāna-element...

Iti 44

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This, bhikkhu, is a designation for the element of Nibbāna: the removal (vinayo) of lust, the removal of hatred, the removal of delusion. The destruction of the taints is spoken of in that way.

The destruction (khayo) of lust, the destruction of hatred, the destruction of delusion: this is called the Deathless.

SN 45.7

Venerable Prayudh Payutto a distinguished Thai Scholar Monk explains that another way of interpreting nirodha is that the phenomena does not arise because it's cause has been eliminated. In that sense nirodha would not entail the cessation or suppression of something that has already arisen but instead there is no arising at all. Like for example in 3rd noble truth - dukkhanirodha - which means that suffering does not arise because the cause for it's arising has been eliminated.

Nirodha is a term that is normally translated as 'cessation' or 'stopping'. It's what happens to suffering in the 3rd noble truth, dukkhanirodha (cessation of suffering) and to all of the other elements of the chain of Dependent Arising.

The context which you refer to is the state of nirodhasamāpatti (attainment of cessation), saññāvedayitanirodha¹ (cessation of perception & sensation) or nibbāna² (quenching or stilling). It is a state where all sensory, corporeal and incorporeal experience ceases. It is the last of the meditative attainments after transcending the four jhānas & the four arupa āyatanas (formless spheres).³