Highly recommend his book Shadows of the Mind -- it's on my list. In summary he believes that consciousness isn't a by-product of computation done by neurons (the traditional view), but rather quantum level effects created by MAP proteins within the brain as a result of this computation:
But perhaps the most interesting wrinkle in Shadows of the Mind is Penrose's excursion into microbiology, where he examines cytoskeletons and microtubules, minute substructures lying deep within the brain's neurons. (He argues that microtubules--not neurons--may indeed be the basic units of the brain, which, if nothing else, would dramatically increase the brain's computational power.) Furthermore, he contends that in consciousness some kind of global quantum state must take place across large areas of the brain, and that it within microtubules that these collective quantum effects are most likely to reside.