Phil major here.
Imagine a being that acted exactly like a human, it spoke, laughed, etc. - everything that you'd imagine a human being to do. However, it does not actually feel or think.
For example, if you were to prick one of these "zombies," they would say "ouch," recoil, perhaps berate you, but the zombie does not actually feel pain - it's a purely mechanical process.
Metaphysics is concerned with the nature of being, properties, identity, etc. What one means by whether such zombies are metaphysically possible is really an answer to the question: are such zombies really any different than how we are?
For more: http://en.wikipedia.org/wiki/Philosophical_zombie