1) There is only one 'thing', call it X, Brahman, Consciousness, God, Self ... or whatever.
2) Despite believing this intellectually, there continues to be the experience that there are separate individuals perceiving, feeling, doing etc. with separate objects. The experience of this body-mind as a 'doer' etc. is as good a definition as any for 'ego'.
3) No matter how much reading, thinking, discussing takes place to reinforce the belief in the reality of the situation, this ego experience persists. i.e. the ability to see beyond the apparent existence of an ego (separate subjects and objects etc.) is not accessible to mind or intellect.
4) The rational justification for this process has been described as Brahman somehow becoming 'identified' with the particular body-mind. The ego experience can be described as the thought 'I *am* this body/person or whatever'. Again, this is sometimes described as the true reality of the situation being obscured by ignorance or avidya.
5) This experience of being an individual could be compared to the experience in a dream of being a different person, say. In the dream, this different identity is firmly believed. On awakening, however, the false reality of the dream is recognised and the 'true' waking reality acknowledged.
6) In an analogous manner, it is possible (but not by design or intent, just as in most dreams) to 'awaken' from the usual waking state of consciousness into recognition of the true nature (of oneness). Then the previous experience is seen as another illusion. This is the removal of the advidya. This true nature is the 'background' on which all of the other manifestations take place, like the cinema screen. This paradigm shift (though not of the intellect) is termed moksha (liberation) or realisation.
7) This is not to say that the waking world in any sense disappears. Everything remains outwardly as it was. The differences are that it is now known (beyond a mere intellectual appreciation) that there is only Brahman (and that 'I am that). It is also known and experienced that there is no doer, perceiver, thinker, desirer etc, although doing, perception, thinking etc. all carry on as before. Thus, for example, as Ramesh Balsekar says, there is still regret if the 'person' does something 'wrong' (but no guilt), still pleasure (but no pride). i.e. There is still experiencing of all the things that were there before but no ego to claim responsibility.