Stare at your hand and try to notice the experience of red. Now try to describe, in the language of neurons and chemistry, what that experience IS. You'll find a strange gap. Brain states are publicly observable, made of physical stuff, locatable in space. Experience is private, subjective, and seemingly not locatable in any obvious physical sense. How do they connect?
Descartes thought they couldn't, really — mind and body must be distinct substances, somehow interacting at the pineal gland. Contemporary philosophers mostly reject substance dualism but disagree on what to put in its place. Physicalists say mental states ARE brain states — qualia (the redness of red) is just a way the brain processes information. Property dualists, like David Chalmers, say physical processes generate experience but experience isn't reducible to them. The "hard problem" of consciousness is exactly this irreducibility.
Eliminativists (the Churchlands) go further: maybe our folk-psychological talk about beliefs, desires, and qualia is just wrong — like talk of phlogiston was wrong — and a mature neuroscience will replace it. Functionalists say it doesn't matter what mental states are made of, as long as they play the right role in cognition. Each view costs something — and no one currently knows how to close the explanatory gap between objective brain and subjective mind.