He talks about consciousness as an epiphenomenon, where the pattern itself is what makes something conscious, rather than some magical property that some matter has and other matter doesn't. With mathematical precision, he describes how consciousness relates to the ability to self-reference and how this relates to fundamental paradoxes in various fields such as the Halting Problem, Godel's Incompleteness Theorems, Russel's Paradox, and the works of Escher and Bach.
This line of thinking brings up some very interesting moral questions: What is it about life that makes us want to value it? Why do we have the notion of "higher" and "lower" life forms and value some species more highly than others? If we created a sufficiently advanced AI, that gave all the appearances of having feelings, a sense of self preservation, an identity, and desires, would it be immoral to unplug it or control its freedoms? What if it felt and understood even more than a human? Would its needs supersede our own?
Anyway, I highly recommend that book, GEB. It has made most other philosophizing about consciousness seem flat to me.