The concept of the philosophical zombie is one that was popularised by David Chalmers and discussed at length in Chalmers 1996. Since then the idea has been the subject of much debate with numerous classes of zombie and zombie world having been proposed. There is considerable disagreement as whether zombies are possible/conceivable and what it would mean if they were.
A philosophical zombie is the same as any other person except they lack phenomenal consciousness and its associated qualia. Although not explicitly part of the definition, it seems reasonable that such zombies would also lack free will.
Conceivable vs Possible
Much of the debate about philosophical zombies centres around whether they are conceivable and/or possible. These two terms have similar but not identical meanings.
Something is said to be conceivable if we can imagine it. However just because we can imagine something doesn’t mean that it could exist in the real world; if it could then it is said to be possible. If it could exist in some real world, not necessarily ours, then it is said to be metaphysically possible.
An example of something that is conceivable but not possible is travel faster than the speed of light (FTL). This is clearly conceivable and is a foundation for much science fiction. However, according to our current science, it is not possible in our universe. Whether or not FTL travel is metaphysically possible is a matter of debate.
When it comes to things that are possible but not conceivable, one example might be quantum physics. Scientists know the mathematics behind it, but an intuitive mental model of what it actually means is beyond most people. Consciousness itself might also belong to the “possible but not conceivable” category, a position espoused by mysterianism.
So where do philosophical zombies fit in all this? That depends on who you ask. Physicalists tend to argue that philosophical zombies are simply not possible in this or – sometimes – in any world. Some even argue that they are not even conceivable because our conception of them misrepresents consciousness.
Other people, notably dualists, believe that philosophical zombies are not only conceivable but actually possible, either in our world or some other.
References:
Chambers, David J. The Conscious Mind (OUP, 1996)