The thought experiment
A philosophical zombie, or 'p-zombie,' is a hypothetical creature that is molecule-for-molecule identical to a normal human and behaves in exactly the same way, yet has no inner experience whatsoever. It would say 'that coffee smells wonderful,' flinch from a hot stove, and discuss its feelings, all while there being nothing it is like to be it on the inside. The lights, so to speak, are off.
The idea was made central to modern philosophy of mind by David Chalmers in the 1990s. The key move is not that zombies exist, or ever could in our world, but that we can coherently imagine them. If a being physically just like us but lacking experience is even conceivable, that seems to show experience is an extra fact, not something guaranteed by the physical wiring alone.
Why philosophers care: the hard problem
This connects directly to what Chalmers named the hard problem of consciousness: why is there any felt experience at all, rather than just information processing in the dark? The zombie argument is meant to show that no purely physical story, however complete, logically forces experience to appear. You could specify every neuron and still, the argument claims, leave out whether anything is felt.
If that is right, it challenges the view that the mind is nothing more than the brain's physical activity, and suggests consciousness might need its own place in our picture of nature. That is a large conclusion to draw from an act of imagination, which is exactly why the argument is so debated.
The main objections
Daniel Dennett is the best-known critic. In his essay 'The Unimagined Preposterousness of Zombies,' he argues that people only think they can conceive of a zombie because they are not imagining it fully. Once you include every functional detail of a system that monitors and reports on its own states, Dennett contends, you have described everything consciousness could be; there is no leftover 'experience' to subtract. On his view the zombie is not genuinely conceivable, just superficially so.
Others argue that conceivability does not reliably tell us what is truly possible: we can imagine many things that turn out to be incoherent on closer inspection. The debate remains unresolved and is one of the sharpest fault lines in the study of mind. Whether you find zombies illuminating or preposterous tends to track whether you think experience is something over and above physical function.