David Barash thinks it's the question of how the brain creates subjective experience:
[T]here are lots of other hard problems, such as the perennial one of reconciling quantum theory with relativity, whether life exists on other planets, how action can occur at a distance (gravity, the attraction of opposite charges), how cells differentiate, and so forth. But in these and other cases, I can at least envisage possible solutions, even though none of mine actually work. But the hard problem of consciousness is so hard that I can’t even imagine what kind of empirical findings would satisfactorily solve it. In fact, I don’t even know what kind of discovery would get us to first base, not to mention a home run.