It is an expression that is used especially in various places in the bṛhadāraṇyaka upaniṣad.

It means that I understand that objects (this) do not stand alone, and all refer to the deeper substrate consciousness. If I understand that all things are in themselves an expression of consciousness, I can effortlessly apply 'neti neti'. It thus denies everything that can be objectified, physical or subtle.

To say neti neti is actually to say: This object, that object (iti iti) is me, consciousness, too. But it is not me as such, not as a separate object. Individual objects as such I may deny, as being, not what it seems to be.

Because there is no point in denying everything. This only leads to psychological dissociation. If everything is denied as being only appearances, expressions of the truth, we must also be told what the truth is. We also need to know what atma, the self is. For that we have the mahā-vākyas, the great theses. Such as 'I am brahman' (aham brahmasmi), or 'you are that' (tat tvam asi).

To understand the relationship between what I may deny as myself, and what I am, the concept of mithyā is important. This means that all objects are relative: Impermanent, changeable and especially dependent on satya, the independent consciousness. Since only the self (ātman) is satya, i.e., imperishable, unchanging and independently real, the whole universe as such is denied as not really real. Denial of objects does not mean that there is nothing. No, there is only being. Names, forms and functions are no more or less than borrowed existence from existence itself. Like a dream in the dreamer, like a mirage in the desert, like a wave in the water, etc.

All objects are an expression of myself, consciousness, the only being, that to which the terms ātman, brahma, sat cit ānanda refer. How? A pot is actually its deeper substrate, clay. All the names, forms, and functions, are actually their deeper substrate consciousness. How is that possible? Because all the names, forms, and functions are nothing but elaborations, concepts of the pure intelligence that is consciousness. And pure full consciousness you are. Tat tvam asi.

Consciousness is unchanging and is not limited by the apparent forms it can take. Just as an ocean is not limited by its waves, which are no more than temporary appearances in it. By carefully putting aside everything that is impermanent and objectifiable (and thus untrue because it is not really real), the non-objectifiable, unchanging truth is implicitly revealed.

Neti neti is also called bādha, denial because it is dissolved into a subtle whole. (Sublimating objects in their true nature, sublimating, see abādha and bādha). Lifting is actually lifting the apparent blanket of matter, into the light that it really is, although it didn't really cover me. You do this with knowledge, so just by knowing that it is so, even if it seems otherwise (ignorance).

This is also how apavāda vākya works, the denial of an earlier statement. A concept can express a truth, but the truth is not a concept, but unknowable, and only what I am. As long as we are still expressing something, it is not, and yet we have to go through the concepts, to discover knowledge, and to be the truth.

All in all, it is important to state that with neti neti I do not say goodbye to all objects, but that I realize that they are all me, myself, consciousness. All objects turn out to be myself. Other people too. Only with this non-dual vision, I can easily love everything unconditionally. That is non-dual devotion. Because I, consciousness, is all there is. Objects are also this knowledge. Brilliant conclusion: 'Since the spectre of ignorance haunts consciousness, I love it unconditionally'.