Qualia is a term describing the actual _feeling_ of something as consciously perceived. Wikipedia explains it better: http://en.wikipedia.org/wiki/Qualia
The problem is this: Consider perceiving the color red. An outside observer can explain this as photons hitting my eye and me reacting. The only problem is, I can actually see the color. How can a series of chemical reactions cause me to feel?
The irony of this is, of course, that pzombies (philosophical zombies: beings that don't feel anything but act exactly as though they do) would come to the same conclusion.
Since it is impossible for anyone other than myself to verify that I exist as anything more than a series of chemical reactions (ie. I actually feel), it is a difficult problem to work with.
I, for my part, was led to the conclusion that the scientific-materialist perspective was wrong, or at least grossly incomplete. It seems logical as science is essentially the art of useful fiction: we make up the simplest story that predicts the right answers and use it until it breaks (and sometimes beyond that and just avoid the points we know it breaks at).
I'm very interested in hearing others' views.