Spoiler alert: The whole realization is that the entire concept of you is artificial. The idea that there is an ever-present unchanging thing called "you" is fairly straightforward for the uninitiated to grasp. The idea that there is no "you" separate from "me" is harder— by a lot.
What attracted me to it was how well it blended in with our modern ideas in physics. Not just the idea that a wavefunction never dies to zero (unless there is a truly infinite potential somewhere), and that we are part of a large many-body system. But also the idea of the big-bang at the universes (re-?)conception: That spacetime itself started at a point and expanded. It is one thing- a big blob of clay- out of which lumps are formed. One is you and one is me. But we are connected. Your existence would be different if I didn't exist.
To kill the ego is to come to an intuitive understanding of this- by being aware and present.