Defence Against the Dark Arts is a class offered at Hogwarts that, understandably, teaches the students how to defend themselves against dark magic. It has a notorious reputation of burning through teachers like a brushfire through California.
There seem to be two types of lessons that are taught in DADA: offensive/defensive spells, and protection from dangerous magical creatures, though dangerous creatures as a primary foe was mostly emphasized in the early books. This may have been because with the threat of Voldemort and dark arts all but snuffed, nasty creatures were seen as a remaining threat.
In crossover fanfic, especially crossover fic that replaces one of the books by bringing in an outside character as a teacher, expect that character to teach DADA. Though sometimes they have taken over History of Magic if they're feeling frisky.
Due to the fact that the main character of the books is shown as having a natural talent for DADA, many Sues will be shown as also excelling in the subject or possibly even teaching it.