The SEP article on Zombies writes:
Zombies in philosophy are imaginary creatures used to illuminate problems about consciousness and its relation to the physical world. Unlike those in films or witchraft, they are exactly like us in all physical respects but without conscious experiences: by definition there is ‘nothing it is like’ to be a zombie. Yet zombies behave just like us, and some even spend a lot of time discussing consciousness.
Few people think zombies actually exist. But many hold they are at least conceivable, and some that they are possible. It is argued that if zombies are so much as a bare possibility, then physicalism is false and some kind of dualism is true. For many philosophers that is the chief importance of the zombie idea.
Why is it true that if zombies are possible that physicalism must be false, and which—if any—philosopher's have actually contended that zombies are possible, rather than merely conceivable in a vague sense?