As discussed (a long time ago now) on my Consciousness page, the phenomenon of consciousness stands out as being entirely unexplained by the current paradigm in science. Yes, we can say that certain experiences correlate to certain brain states: this bunch of neurons firing happens at the same time as the user of that brain reports some repeatable experience. But no, we have no theory whatsoever as to how anything material (such as electrical signals, molecules bouncing, chemical reactions, information processing, space warping), can be experienced, at all.
Think about it: why should a bunch of molecules and electrons moving about or computing in your brain feel something? This is what is known as the ‘hard problem’ of consciousness. The easy problem is to show that experiences correlate with brain states. The hard problem is to show why.
Peter Russell doesn’t know why, either. However, he points out that given the current paradigm of science doesn’t have even the slightest handle on consciousness, something may be wrong with that paradigm. Science as currently understood regards matter, time and more especially energy and space (including multiple dimensions and so on), as the fundamental building blocks from which the Universe appears to be made. What if this is wrong? He suggests instead that consciousness itself is the fundamental ground of reality.
This is not as crackers as it might sound at first, as he explains in his lecture, and respectable philosophers such as David Chalmers have made similar suggestions (in his case, that information might be fundamental). If one’s current assumptions don’t work, and in this case they clearly don’t, then they need to be reconsidered.