If you've not run across the idea of the science of consciousness before, it seems to stem from the idea that a lot of the things we think go on in our heads actually go on in our brains, too. That is, things like ideas, wishes, feelings and such have been found to correspond with actual neural activity in the brain. This means that technically, it's impossible for someone to have a "brainless idea," Jersey Shore and the Wisconsin State Senate as evidence to the contrary notwithstanding.
"Consciousness" in this kind of discussion usually boils down to some kind of talk about how people are aware they're people, and how they think about that. Sometimes. In other words, squirrels spend zero time thinking about what makes a good squirrel or about whether or not they've achieved that status. Dogs may be concerned with whether or not we tell them that they're good dogs, but that has more to do with them worrying about whether or not we'll kick them out of the pack than it does with formulating their own ideas about what good dogs are. A "science of consciousness" tries, among other things, to explain all those thoughts and feelings, as well as art, music and nearly everything else, in terms of neural activity in the brain.
The books Dr. Tallis reviews suggest that our human consciousness also has some sort of biological function, or else we wouldn't have it. Just like long claws and sharp teeth serve the lion, strong leg muscles and lightweight build serve the antelope and the ability to stink serves the skunk, our consciousness must also serve us, giving us some biological edge over our competitors. Dr. Tallis is unconvinced -- his own understanding suggests that whatever biological edges we may gain from consciousness could have been gained without it.
I'm unconvinced too. There are lots of life forms that thrive without consciousness, like roaches or (insert cheap joke about pop culture celebrity, politician or other person you'd like to take a dig at here). Consciousness isn't biologically necessary, even if it is helpful to be able to build spears and clubs when you're slow, small, climb poorly and have short teeth and claws. Now, Dr. Tallis is, as far as I can tell, an atheist, which means he wouldn't track with me beyond this point. For me, consciousness is an evidence of God's presence: Life does not need consciousness to exist, but it does need consciousness to know God.
That's one of the reasons I don't much sweat the idea of life evolving over time like some of my fellow believers do, although I cast no stones their way over their preferences. I have no problem with the idea that God created the universe pretty much according to what modern cosmology, archaeology and biology tell us about it. And if God did so that way, then to me the presence of beings in that universe who can wonder about God, the universe and themselves is a sign of God's reality. Not proof, because I'd be assuming as true the thing I was trying to prove was true, which you can't do in the proof game.
Just a sign.