It's short for "I accept your challenge." Which is really short for "what you just said was objectionable and we can settle this on the field of honor" (or, as Semy_of_pearls says, any type of competition).

What I'm trying to get at, and may not have articulated well, is that it's a clear way for people who don't understand social cues or niceties (and the rest of us, too) to know that they have crossed the line into ungraceful behavior.