What is 'letting go' and 'detachment' actually?

Anything comes naturally and goes naturally.

(1) Awareness remains uncaught, not starting to cling to a pleasant feeling.

As when we focus on it, singling it out - and losing the wholeness of the unlimited space. I think, singling out and losing the whole is the mechanism of attachment.

And that's how it leads to ignorance. Enclosing a feeling, we create limited view. Is it creating a mental construction around that sensory pleasure?

(2) Awareness remains uncaught, not trailing a deluded thought with more deluded thoughts.

(3) Awareness remains uncaught, not creating unnecessary constructions.

(Which would enchain the mind, making it busy, rigid and limited).

A Tibetan Teacher described different levels of mastery in letting go of thoughts as snow falling on earth, water and fire. Snowflakes falling on earth lie for some time, creating a layer of snow, even if it gradually melts. Snowflakes falling in water melt instantly. Snowflakes falling over fire melt even before they touch anything.

With mastery we can notice unnecessary thoughts when they only start to condense. It can be likened to a tablecloth and wrinkles. We don't need to deal with each wrinkle, as if it was real separate object. We can just pull a bit the cloth, and it's flat again. Perhaps it's a way to observe emptiness of mental creations.

Not creation of constructions, not re-creation of trains of thoughts and vexations... It can be called letting go - of the circular processes of samsaric thinking. In the sense: we don't keep these processes.

About letting go in Zen practice: http://www.chancenter.org/chanctr/ddp/channews/09-1982.html

There are different words here, such as:

'Nekkham­ma', which generally refers to 'renunciation' of sensual pleasures (eg. 2nd path factor).

'Pahānā' (SN 45.8 right effort) & 'pahāya' (MN 38 hindrances) & 'pajahati' (AN 3.40; SN 35.101), which generally refers to abandoning hindrances & unwholesome qualities.

'Anupādā': not taking as one’s own, not holding on to.

'Vossagga', which means 'giving up', 'relaxation', 'handing over' or 'surrender', and is generally found in meditation instruction about the (preliminary) development of the path, such as in SN 48.10 & end of MN 118; & found in DN 31 in respect to a husband giving (surrendering) authority to the wife in the home or an employer giving employees a share in profits .

a monk, a noble disciple, making letting go (vossagga) the meditation object, attains concentration, attains singleness of mind.... SN 48.10

'Paṭi­nissag­gā', which means means 'relinquishment' or 'giving back', possibly 'returning back', and is generally found in the fruition of the path, such as in 3rd noble truth (below), last (16th) stage of Anapanasati or in definitions of Nibbana (below).

the noble truth of the cessation of suffering: it is the remainderless fading away and cessation of that same craving, the giving up and relinquishing of it, freedom from it, nonreliance on it.

dukkhanirodhaṃ ariyasaccaṃ — yo tassāyeva taṇhāya asesa­virāga­nirodho cāgo paṭinissaggo muttimutti anālayo.

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sabba­saṅ­khā­ra­sama­tho sabbū­padhipa­ṭi­nissaggo taṇhākkhayo virāgo nirodho nibbānaṃ

Calming of all formations, the relinquishing of all acquisitions, the destruction of craving, dispassion, cessation, Nibbāna

Ultimately, 'letting go' means to not take something as 'being onself' or 'belonging to oneself', as summed up in SN 35.101:

Suppose a person were to gather or burn or do as he likes with the grass, twigs, branches, & leaves here in Jeta's Grove. Would the thought occur to you, 'It's us that this person is gathering, burning, or doing with as he likes'?

No, lord. Why is that? Because those things are not our self nor do they pertain to our self.

In the same way, monks, the eye is not yours: let go of it. Your letting go of it will be for your long-term happiness & benefit... The ear... The nose... The tongue... The body... The intellect is not yours: let go of it. Your letting go of it will be for your long-term happiness & benefit... Whatever arises in dependence on intellect-contact, experienced either as pleasure, as pain, or as neither-pleasure-nor-pain, that too is not yours (na tumhākaṃ): let go of it (taṃ pajahatha). Your letting go (pahīnaṃ) of it will be for your long-term happiness & benefit.

SN 35.101