A philosophical zombie or p-zombie is a hypothetical entity that looks and behaves exactly like a human (often stipulated to be atom-by-atom identical to a human) but is not actually conscious: they are often said to lack phenomenal consciousness.
A p-zombie is as likely as anyone else to ask, "When I see red, do I see the same color that you see when you see red?", but they have no real experience of the color red; the zombie's speech must be explained in some other terms which do not require them to have real experiences.
The zombie thought experiment is purported to show that consciousness cannot be reduced to merely physical things: our universe is purported to perhaps have special "bridging laws" which bring a mind into existence when there are atoms in a suitably brain-like configuration.
Physicalists typically deny the possibility of zombies: if a p-zombie is atom-by-atom identical to a human being in our universe, then our speech can be explained by the same mechanisms as the zombie's — and yet it would seem awfully peculiar that our words and actions would have an entirely materialistic explanation, but also, furthermore, our universe happens to contain exactly the right bridging law such that our utterances about consciousness are true and our consciousness syncs up with what our merely physical bodies do. It's too much of a stretch: Occam's razor dictates that we favor a monistic universe with one uniform set of laws.
Other physicalists accept the possibility of p-zombies, but insist that we are p-zombies and consciousness is an illusion.
Non-physicalists use the apparent conceivability of p-zombies to argue that it is impossible to explain how phenomenal consciousness arises using physical facts alone. P-zombies are presumably not possible in our universe, but they are conceivable (on this view) because a physically identical universe with different psychophysical bridging laws or different quiddities could indeed harbor p-zombies.