It's kind of supposed to be hard to explain, but...hmmmm...maybe something like "why is there a subjectively perceived difference between sleepwalking through your life and being awake?" If we imagine a sort of "perfect sleepwalker" who, while sleepwalking, could hold conversations, go to work, write poetry, and do anything else that people do while awake exactly as waking people do it - even to the point where if we ask her "Are you awake?" she answers "Yes." - then it might be necessarily impossible for us outsiders to distinguish her sleep from her waking. But we feel an intuitive believe that she should be able to do so easily. If she's awake, she can notice her awakeness and all the sensations she's feeling and experiences she's having. If she's sleeping, then it doesn't even make sense to "experience" not being awake, because there's no one "at home" to do the experiencing. An equivalent interpretation of the problem revolves around qualia. Suppose that your experience of "red" was everyone else's experience of "blue". You would never be able to confirm this by talking to other people - you would say things like "blue is the color of the sky and the sea and short-wavelength light" and they would agree with you, but you would be thinking of red when you said it, and everyone else would be thinking of blue. This "experience of blue" which is separate from statements about blue or concepts surrounding blue is the "quale" (plural "qualia") of blue. Intuition tells us one difference between the sleepwalker and the awake person is that if you ask the sleepwalker what color a stop sign is, the light rays would hit her eyes, go through a chain of neurons in her brain, and produce the response "it's red". The same thing would happen in the awake person, but she'd also have the conscious visual experience qualia thing where she "sees" a certain color in her "mind's eye". The hard problem is whether there's a difference between awake people with qualia and perfect s

I find David Chalmers's explanation of what is meant by "qualia" and "subjective experience" and "something its like to be" the easiest to understand. For example, read the first chapter of The Conscious Mind. The Knowledge Argument above refers to the fictional story of Mary the color scientist. She was raised in a black and white environment and never saw color. But she read textbooks on color theory (printed in black and white, of course.) The question is, when she finally experiences the color blue, how is that different from the previous knowledge she had about what the color blue would be like? That different extra aspect to the actual experience is what we refer to as qualia, and how such an experience can be caused by physical processes is (in Chalmers's terminology that has now been widely adopted) the Hard Problem.