What is initial thought and discursive thought

Initial thought and Sustained thought is NOT a THOUGHT. The translation in my opinion is very misleading.I personally use the Pali Word Vitakka and Vicara.

When Jhana States arise there is no thinking.This is too gross of an activity.

The only way i can explain Vitakka-Vicara is Try lifting your arm.

Now you know that intention/will/urge...before you lifted your arm.Before you thought of lifting your arm.

Underneath thoughts.

There is a subtle movement.

Layered below thoughts.Thats Vitakka-Vicara.its like a pulling and pushing movement when your playing with a rope,without thoughts.Before thoughts.Just instinct.That's it Basic Instinct.This is present in first Jhana.

In the second Jhana the will is removed so now its Really immovable.

It is a very good question that you asked @DeusIIXII, regarding initial thought and discursive thought. In Pali it is Vitakka-Vicāra: It is good to know about 'thought-conception and discursive thinking', both within Jhana and outside of it. Within the context Jhana, only in the first Jhana it comes as one of the five factors. The five factors are… Initial application (vitakka), sustained application/ discursive thought (vicara), joy (piti), happiness (sukha), and one-pointedness (ekaggata). The second Jhana has the three factors of piti, sukha, and ekaggata. The third Jhana has the two factors of sukha and ekaggata. If you want to refer to a Sutta:

SD 24.11 _ Pathama Jhana Pañha Sutta or (Savitakka) Pathama Jhana Sutta. Progressing in the 1st dhyana.
SD24.12a _ Dutiya Jhana Pañha Sutta or (Avitakka) Dutiya Jhana Sutta. Progressing in 2nd dhyana.

The key-note of Buddhism is this right understanding. Clear vision of the four noble truths or right understanding leads to clear thinking, samma samkappa. Thoughts or samkappa always comes in the form of a seed conception, or first idea, or initial thought -is meant the vitakka mental state. A mind intent only on issues related to the breath, not pulling any other objects in to interfere, until the breath is refined, giving rise to fixed absorption and then liberating insight: This is Right Concentration. Also this act of thinking through of the initial idea of breath is Vicāra. So Here the breath is the vitakka, the initial thought. To adjust the breath and let it spread, is really thinking called vicara, evaluation.

Outside of meditation try to understand it this way.
Sankharas are the kammically active volitions responsible for generating rebirth and thus for sustaining the onward movement of samsara, the round of birth and death. In this context sankhara is virtually synonymous with kamma. Sankharas in dependent origination is put into three types: bodily (inhalation and exhalation), verbal ( Vitakka-vicāra: 'thought-conception and discursive thinking'), and mental [feeling (vedanā) · perception (sañña) ]. Sankharas are divided into the meritorious and demeritorious. Sankharas, propped up by ignorance and fueled by craving drive the stream of consciousness onward to a new mode of rebirth, where consciousness becomes established determined by the kammic character of the sankharas. With good deeds the sankharas or volitional formations will propel consciousness toward a happy sphere of rebirth, and with demeritorious deeds, the sankharas will propel consciousness toward a miserable rebirth.

If you are to take this second of the three Sankharas …. verbal ( Vitakka-vicāra: 'thought-conception and discursive thinking'), Before one speaks aloud, there is a ‘speaking’ or contemplation that takes place internally. The first or initial contemplation of a thought is ‘vitakka’, then we ‘think through’ or further the internal ‘speaking’. We call it consideration, or ‘vicāra’. Thus the contemplation is considered to be the vitakka/vicara. Another name for it is vaci‐sankhara or verbal fabrication. So the two basic verbal sankharas are directed thought and evaluation - vitakka & vicara.

Ordinarily, when unrelated to jhana, the words 'vitakka' & 'vicara' simply mean 'thought', 'thinking' & 'thinking about'. For example, MN 19 is about 'two kinds of thinking'; MN 20 is about distracting thoughts &, in MN 44, 'vitakka' & 'vicara' are called the 'verbal conditioner' because they cause speech to occur, as follows:

Having first directed one's thoughts and made an evaluation, one then breaks out into speech. That's why directed thought & evaluation are verbal fabricators. MN 44

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In the context of jhana, the words 'vitakka' & 'vicara' have a different & special meaning. Here, they do not refer to ordinary verbal thinking but to non-verbal movements of mind that finalise the attainment of & maintain the 1st jhana.

In respect to the attainment of the 1st jhana, 'vitakka & vicara' refer to 'applied & sustained thought', where the mind itself (rather than volitional intention) applies itself to bring to fruition the 1st first jhana. As said, these movements of mind are beyond the scope of ordinary volition.

Once the 1st jhana comes to be, 'vitakka & vicara' refer to 'directed thought & pondering / exploring / moving about ', where part of the mind itself remains active in examining & responding to its own response to the jhana factors (such as rapture), to ensure the jhana is maintained.

As stated in SN 48.10, jhana is born from 'letting go' ('vossagga'). Thus, 'vitakka & vicara' ('directed thought & pondering') operate in the 1st jhana to ensure the letting go & thus the jhana factors are maintained. Refer to Ajahn Brahm's explanation, here, about the "wobble".

There are many subtle different explanations of vitakka & vicara in respect to the 1st jhana. For example, the monk Thanissaro has translated with the words 'directed thought & evaluation'; and Buddhadasa had translated (from Thai) with the words 'noting' & 'experiencing' (here) and 'looking at' & 'knowing thoroughly' (here).

I personally prefer Ajahn Brahm's explanation because the existence of vitakka & vicara in the 1st jhana simply indicate the mind is not completely still, despite its attainment of 'one-pointedness'.

I also like Jeffrey Brooks summation as "sustained application of a meditation technique" (namely, the now automatic technique of 'letting go' ) but I do not agree with Jeffrey's translation of 'sustained attention' because the mind has 'attention' in every jhana:

The correct translation of the Pali terms 'vitakka' and 'vicára,' with respect to the absorptions (jhanas), must be "applied and sustained attention" or "sustained application" of a meditation technique."

Jeffrey Brooks

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'One-pointedness' refers to the mind becoming unmovingly glued to a mental image ('nimitta'), which has arisen to replace the totally tranquilised breath as the object of meditation. This 'one-pointedness' can be compared to an axle upon which a wheel becomes fixed to. Although the wheel is fixed to the axle and cannot move off the axle, the wheel can still spin around the axle.

Similarly, although the mind is fixed or unmoving due to one-pointedness (which also results in ordinary volition ending), the mind itself can still actively move towards & away from the other factors of jhana. These movements of mind that sustain the meditation are 'vitakka & vicara'.

In conclusion, understanding what 'vitakka & vicara' are as factors of jhana will not assist in the attainment of jhana because these factors of jhana occur beyond the sphere of ordinary volition, as Ajahn Brahm has explained.

For example, in the preliminary development leading to jhana, a more primitive 'vitakka & vicara' refers to the volitional activity that keeps 'letting go'; that keeps wilfully non-attaching. But once jhana is reached, ordinary volition falls away and a new 'automatic volition' arises.