In other words, when you see a red surface or feel a pain which part of the brain is activated by that experience. The "hard" problem, so named by David Chalmers in 1995, is the problem of explaining what sensations like red or pain actually are and how a material brain can produce an immaterial sensation like color or sound.
The "hard problem" is, in other words, the problem of explaining what consciousness is and where it comes from.
Michael Hanlon at Aeon elaborates:
Nearly a quarter of a century ago, Daniel Dennett wrote that: ‘Human consciousness is just about the last surviving mystery.’ A few years later, Chalmers added: ‘[It] may be the largest outstanding obstacle in our quest for a scientific understanding of the universe.’ They were right then and, despite the tremendous scientific advances since, they are still right today.Perhaps, as Denyse O'Leary muses at Mind Matters, the problem with trying to solve the hard problem is the underlying materialistic assumption that consciousness is explicable in terms of material substance, that somehow matter (the brain) produces consciousness.
I do not think that the evolutionary ‘explanations’ for consciousness that are currently doing the rounds are going to get us anywhere. These explanations do not address the hard problem itself, but merely the ‘easy’ problems that orbit it like a swarm of planets around a star.
The hard problem’s fascination is that it has, to date, completely and utterly defeated science. Nothing else is like it. We know how genes work, we have (probably) found the Higgs Boson; but we understand the weather on Jupiter better than we understand what is going on in our own heads. This is remarkable.
Consciousness is in fact so weird, and so poorly understood, that we may permit ourselves the sort of wild speculation that would be risible in other fields....We can speculate that it is consciousness that gives rise to the physical world rather than the other way round. The 20th-century British physicist James Hopwood Jeans speculated that the universe might be ‘more like a great thought than like a great machine.’
Idealist notions keep creeping into modern physics, linking the idea that the mind of the observer is somehow fundamental in quantum measurements and the strange, seemingly subjective nature of time itself, as pondered by the British physicist Julian Barbour.
I don’t know. No one does. And I think it is possible that, compared with the hard problem, the rest of science is a sideshow.... The hard problem is still the toughest kid on the block.
Perhaps things are the other way around. Perhaps mind is fundamental and matter is somehow a product of immaterial mind.
O'Leary writes,
Almost certainly, the human mind is not a material entity but an immaterial one, like information. If we accept that, we can perhaps convert it from an opaque mystery that can never yield any results because we are on the wrong track to a mystery that is difficult but solvable in principle because we are now looking in the right places.
