Paper cuts are usually razor-sharp cuts, usually to your fingers, as a result of running an edge of paper along your skin, so that the thin edge of the paper cuts into you. For some reason, they are usually quite painful, probably because they are usually on fingers, which tend to have more nerve endings than most of the rest if the body.

I've been told, but haven't tried this myself, that using super glue to close a paper cut is usually the best way to alleviate the pain, though I have no idea if it affects the healing process negatively.