What is actually Nirvana -- what are some Tripitaka sources?

I associate it with cessation -- with the ending of dukkha, of craving -- outlined in the first three noble truths.

It could be, Ānanda, that a mendicant gains a state of immersion such that they have no ego, possessiveness, or underlying tendency to conceit for this conscious body; and no ego, possessiveness, or underlying tendency to conceit for all external stimuli;

Siyā, ānanda, bhikkhuno tathārūpo samādhipaṭilābho yathā imasmiñca saviññāṇake kāye ahaṅkāramamaṅkāramānānusayā nāssu, bahiddhā ca sabbanimittesu ahaṅkāramamaṅkāramānānusayā nāssu;

and that they’d live having attained the freedom of heart and freedom by wisdom where ego, possessiveness, and underlying tendency to conceit are no more.

yañca cetovimuttiṃ paññāvimuttiṃ upasampajja viharato ahaṅkāramamaṅkāramānānusayā na honti tañca cetovimuttiṃ paññāvimuttiṃ upasampajja vihareyyā”ti.

“Ānanda, it’s when a mendicant thinks:

“Idhānanda, bhikkhuno evaṃ hoti:

‘This is peaceful; this is sublime—that is, the stilling of all activities, the letting go of all attachments, the ending of craving, fading away, cessation, extinguishment.’

‘etaṃ santaṃ etaṃ paṇītaṃ yadidaṃ sabbasaṅkhārasamatho sabbūpadhipaṭinissaggo taṇhākkhayo virāgo nirodho nibbānan’ti.

AN 3.32

Perhaps there are people who think that this means ...

1. Meditate (samādhi), and while doing so,
2. Don't be possessive towards the body (saviññāṇake kāye) nor towards all signs (sabbanimittesu)

... and therefore something something something "atta" or real self which is neither the body nor signs. But I don't know (i.e. I don't know a reason to agree with a doctrine of atta like that) -- because I associate self-views and attachment (possessiveness) with dukkha -- e.g. "this is mine ... no, now I've lost it, that was mine, so now I'm unhappy" -- and therefore, cessation of that (nibbana) is necessarily without such "self" and "possessiveness" and so on. If nibbana is uncompounded I'm not sure why you'd want to add an atta concept to it, but "to each his own" I suppose (see also this paper on the subject of whether nibanna is anatta).

Incidentally my concept of nibbana wasn't formed by the sutta above, so don't read into it more than I have -- I'd never read it before, I just looked up a reference (to answer this question) and picked the first one (on this page) which didn't seem to contradict my preconception.

Given that nibbana is uncompounded I doubt it exists in relation to anything else ... but other things can co-exist with it, e.g. to the extent that the Buddha could co-exist with unenlightened beings ... it's not like another place, exactly, more like a different state of mind or something.

I just called it "a state of mind" except that maybe it's better described as a non-state -- e.g. not defiled, without hindrances (klesas).

I wondered about saying that "anything that's not nibbana is a hindrance" (as if nibbana were a pure substrate or element, and everything else were a hindrance or an obscuration on top of that), however, I'm not sure how compassion for example relates to nibbana.

I've also recently seen it described as a state of ethics.

That's it, more or less: simple doctrine. When the Buddha says, "Both formerly & now, it is only dukkha that I describe, and the cessation of dukkha.", then nibbana is the cessation of dukkha.

Oh yes, its selflessness makes it "deathless", also.

Saying that it's without this, without that, only cessation, might make it seem austere or sound like death or something, but I should think that's obviously not the right view of it (see Bhagavā).

Apart from seeing it simply as a state of mind, I think there are other views of it -- but, the following seem to me complications that are maybe more trouble (confusion) than they're worth:

• Ayatana Nibbana

  For example:

  When the five aggregates perish, the anupadisesanibbanadhatu of Lord Buddha appears, dwelling perpetually at the center of Ayatana Nibbana, sitting on a raised diamond throne.

  Bhikkhu Bodhi puts this more prosaicly, but still something implied to be super-mundane:

  Philosophical Dimension of Nibbana

  The Buddha also refers to Nibbana as an 'ayatana'. This means realm, plane or sphere. It is a sphere where there is nothing at all that corresponds to our mundane experience, and therefore it has to be described by way of negations as the negation of all the limited and determinate qualities of conditioned things.

  I don't know what to make of this -- it sounds complicated or florid -- except I agree it's related with negation (or cessation), and I suppose there is some ayatana involved to the extent that nibbana is perceptible.

  You might want to argue that nibbana is a thing (a sense-object) which we can't perceive it directly, but only perceive its side-effects (e.g. cessation of dukkha) -- I'm not sure why that's a useful argument though and anyway maybe all senses are like that, i.e. sensual perception is indirect by nature, in that it is via the senses.

  Perhaps (or presumably) it refers to some meditative experience.

• Nibbana dhatu

  Ven. Bodhi again:

  The Buddha also refers to Nibbana as a 'dhatu,' an element, the 'deathless element' (amata-dhatu). He compares the element of Nibbana to an ocean. He says that just as the great ocean remains at the same level no matter how much water pours into it from the rivers, without increase or decrease, so the Nibbana element remains the same, no matter whether many or few people attain Nibbana.

  Again, I'm not sure that's useful. It's not a bad simile for explaining nibbana's being unconditioned/unaffected.

• Apart from ayatana and dhatu I might quote the rest of Bhikkhu Bodhi's commentary (with my emphasis added on selected words):

  Regarding the nature of Nibbana, the question is often asked: Does Nibbana signify only extinction of the defilements and liberation from samsara or does it signify some reality existing in itself? Nibbana is not only the destruction of defilements and the end of samsara but a reality transcendent to the entire world of mundane experience, a reality transcendent to all the realms of phenomenal existence.

  The Buddha refers to Nibbana as a 'dhamma'. For example, he says "of all dhammas, conditioned or unconditioned, the most excellent dhamma, the supreme dhamma is, Nibbana". 'Dhamma' signifies actual realities, the existing realities as opposed to conceptual things. Dhammas are of two types, conditioned and unconditioned. A conditioned dhamma is an actuality which has come into being through causes or conditions, something which arises through the workings of various conditions. The conditioned dhammas are the five aggregates: material form, feeling, perception, mental formations and consciousness. The conditioned dhammas, do not remain static. They go through a ceaseless process of becoming. They arise, undergo transformation and fall away due to its conditionality.

  However, the unconditioned dhamma is not produced by causes and conditions. It has the opposite characteristics from the conditioned: it has no arising, no falling away and it undergoes no transformation. Nevertheless, it is an actuality, and the Buddha refers to Nibbana as an unconditioned Dhamma.

  ...

  He also speaks of Nibbana as something that can be experienced by the body, an experience that is so vivid, so powerful, that it can be described as "touching the deathless element with one's own body."

  The Buddha also refers to Nibbana as a 'state' ('pada') as 'amatapada' - the deathless state - or accutapada, the imperishable state.

  Another word used by the Buddha to refer to Nibbana is 'Sacca', which means 'truth', an existing reality. This refers to Nibbana as the truth, a reality that the Noble ones have known through direct experience.

  So all these terms, considered as a whole, clearly establish that Nibbana is an actual reality and not the mere destruction of defilements or the cessation of existence. Nibbana is unconditioned, without any origination and is timeless.

Sorry to disagree; I know that Ven. Bodhi must know more than I do, and that he's paraphrasing suttas, but I don't see that these additional explanations make it easier to understand:

• Saying "a reality transcendent" makes it seem other-worldly and more than it is, perhaps unattainable
• Saying "an actual reality" is kind of OK, maybe you shouldn't imply that it's something other than this reality though, albeit undefiled -- if it's a different reality then I understand the message as, unfortunately, "you can't get there from here"
• Saying "the cessation of existence" sounds like death again
• Saying "not the mere destruction of defilements" sounds odd to me, because I think it is "the destruction of defilements", and that that represents a great achievement and not just "mere".