Two ways of knowing
Science works by taking the view from nowhere: measurements anyone can repeat, described in terms anyone can check. That objectivity is its great strength. But experience is stubbornly first-person. The redness of red, the sting of grief, the taste of salt are known by having them, from a single point of view that cannot be handed to anyone else.
Thomas Nagel made this vivid in 1974 by asking what it is like to be a bat. We could map every neuron in the bat's brain and still not grasp how echolocation feels to the bat, because that knowledge belongs to the bat's point of view. The same holds for you. A neuroscientist could know every fact about your visual cortex and still not thereby know what your seeing is like. The methods of science and the target, felt experience, seem to live in different registers.
Mary the color scientist
The philosopher Frank Jackson dramatized the point in 1982 with a thought experiment. Imagine Mary, a brilliant scientist who knows every physical fact about color vision but has lived her whole life in a black-and-white room. One day she steps outside and sees a red rose for the first time. Does she learn something new?
The strong intuition is yes: she learns what red looks like. If so, then all the physical facts, which she already had, did not add up to that one fact about experience. This 'knowledge argument' is one of the sharpest ways of expressing why felt quality seems to slip through the net of purely physical description. Philosophers still debate whether Mary gains a new fact or merely a new way of grasping an old one, but the puzzle refuses to dissolve.
Is the gap in the world, or in us?
Joseph Levine called this the explanatory gap, and he was careful about what it shows. It may reveal a limit of our current concepts rather than a rip in nature; a genuinely puzzling feature of how we understand things, not proof that experience floats free of the brain.
Others push harder in each direction. Some argue the felt quality is fundamental and no physical story could ever capture it. Illusionists such as Keith Frankish argue the opposite: that our conviction of an unexplainable inner glow is itself the thing to be explained, and once we explain the conviction, nothing mysterious is left over. Many working scientists take a patient middle path, expecting that better theories will slowly narrow the gap the way earlier science demystified life and heat. The honest summary is that this is an open question, one of the deepest we have, and not a settled defeat for science.