Often in Advaita circles we're talking about ending the "I", seeing through the "I". This "I" being spoken of is the individual "I", the "ME", the sense of being a separate individual. This individual "I" is identification - the placing of self-ness upon the body-mind, which is always objective. This "I" must be a thought-belief, a construction of assumption. This "I" is believed to be some soul or individual essence abiding in the body-mind.
This placing of individual self-ness upon that ever-present "I" or "awareness" is itself the concept of the individual. That IS the identification, the very mechanism which seems to construct this individual "I".
What's being pointed out is that the true "I" IS what you are - only it is not the body or mind. It is not a separate being. The true "I" is the light behind perception, the essence of seeing. It has been called "awareness" or "consciousness". If you know "I", you know your true Self already. But what IS this "I"? Is it merely the body-mind?
Here are two examples of expressions about the true "I".
Wei Wu Wei
The eye that sees, the ear that hears, the tongue that tastes are only apparatus, but the "I" that sees, hears and tastes is Reality. We only need to realize that and the first perception becomes satori.
Consciousness, the true 'I,' gets exclusively mixed up with a body and seems, as a result, to become a personal entity that is endowed with Consciousness and Being. It becomes the personal knower, feeler, thinker, doer etc., the 'me.'
There is only the true 'I,' the true Self, Knowing Presence or Consciousness, and it is always only itself. There is nothing other than itself. It is 'One without a second.'