A zombie is a critter that is physically and behaviorally exactly like a human being (or any being that we consider to be conscious) but lacks consciousness. That is a stipulative definition, so don't argue with me about it. Just accept it. I'll use 'zombie' to refer to human zombies and won't worry about cat zombies, etc.
Cut a zombie open, and you find exactly what you would find were you to cut a human being open. And in terms of linguistic and nonlinguistic behavior, there is no way to tell a human being from a zombie. (So don't think of something sleepy, or drugged, or comatose.) When a zombie sees a tree, what is going on internal to the zombie's brain is a 'visual' computational process, but the zombie lacks what a French philosopher would call interiority. There is no irreducible subjectivity, no qualitative feel to the 'visual' processing; there is nothing it is like for a zombie to see a female zombie or to desire her. (What's it like to be a zombie? There is nothing it is like to be a zombie.)
Surely, zombies are conceivable. To conceive one, start with yourself. You, dear reader, are not a zombie. You have feelings. Right now, perhaps, you feel bored or puzzled by what you are reading. Slap yourself across the face to wake up. You felt something, a stinging sensation. Do it again just to be sure. Now subtract off (in thought) the conscious experiences leaving behind your body, its behavior, its environment and all the causal processes disporting themselves between body and environment. What you are now conceiving is a zombie.
Are we zombies? According to John Searle, Daniel Dennett's view is that we are zombies. (The Mystery of Consciousness, p. 107) Although we may appear to ourselves to have conscious experiences, in reality there are no conscious experiences. We are just extremely complex machines running programs. I believe Searle is right about Dennett. Dennett is a denier of consciousness. Or as I like to say, he is an eliminativist about consciousness. He does not say that there are conscious experiences and then give an account of what they are; what he does is offer a theory that entails that they don't exist in the first place.
As Searle puts it: "On Dennett's view, there is no consciousness in addition to the computational features, because that is all that consciousness amounts to for him: meme effects of a von Neumann(esque) virtual machine implemented in a parallel architecture." (111)
Dennett's view implies that conscious states are illusory, as illusory as God, the devil, witches and goblins. In reality, there are no conscious states! But as Searle rightly points out, "where consciousness is concerned, the existence of the appearance is the reality." (112)
I'm with Searle on this one. It is just nonsense to think of consciousness as illusory or merely apparent or as somehow hiding a reality that can be described from an objective, third-person point of view. In agreeing with Searle on this point, I by no means endorse his own theory of the mind — which I find to be quite hopeless. To my mind, John Searle's great merit is that of critic. Better than anyone else, he exposes the nonsense rampant in comntemporary philosophy of mind. And that is a great service, even if he cannot tear himself away from naturalism.