The witness is the contemplative pointer to that in which all experience arises but which is itself never an object of experience. Whatever is observed, there is that which observes. Whatever changes, there is the unchanging in which change appears. The Sanskrit word is sakshi, the seer, the one who sees the seen.
The Atma Bodha and the Aparokshanubhuti work the recognition systematically. The body is not the Atman, because the Atman witnesses the body. The senses are not the Atman, because the Atman witnesses the senses. The mind is not the Atman, because the Atman witnesses the mind. Thoughts arise and pass; the witness does not arise or pass. The Ashtavakra Gita gives the same teaching in a more uncompromising voice: you are the witness only. You have nothing to do with the doer.
The Direct Path teachers (Atmananda Krishna Menon, Jean Klein, Greg Goode, Francis Lucille) take the inquiry further. They ask the practitioner to investigate, by patient experiment, whether the witness is itself an object. Look for the seer, they say, and notice that you cannot find it. The witness is not an object, it is what is doing the looking. And what is doing the looking is what one is.
The recognition that finally lands is that the witness and what is witnessed are not two. There is no separated observer behind the eyes; there is only awareness, and the apparent objects are arisings within it. The seer and the seen are the same Self. This is the conclusion of the inquiry: not the witness as a separate refuge, but the witness as a doorway through which the apparent two-ness dissolves.