Batman is the nom-de-guerre of billionaire industrialist Bruce Wayne; the star of many graphic novels, TV shows, movies, and others. Growing up the son of a very wealthy family, Bruce led a charmed life, until one day, his parents were shot dead outside of a movie theater. At that moment, he vowed to use his fortune to train his mental and physical skills to their peak, and now, Batman fights an ongoing war against crime.
In the official canon; that is. In Drawception, Batman does quite a bit more, whether it makes sense or not. From joining the Ku Klux Klan, to turning around and punishing racists (either way, it seems Batman doesn't think much of animal rights), the caped crusader gets his cape into all manner of hi-jinx on Drawception.
Why? Possibly because of the same reasons Pikachu and Sonic do; he's a very well-known character who's also very easy to draw. It also may be funny to many people because Batman is usually seen as a cold, humorless personality, so seeing him involved in comedic schtick gains a new layer of comedy from its irony. Whatever the original cause, Batman's large presence on the site is now a cherished tradition, and will likely continue to be so.
Subliminal Batman Edit
Many players have also taken to hiding likenesses of Batman in otherwise unrelated games, in such a way that the Batman is not seen until afterwards. See Subliminal Batman
http://drawception.com/viewgame/1O9SZtATDF/batman-mourns-mikko5836/ http://drawception.com/viewgame/xsKNje5kmA/batman-has-been-in-a-paintball-fight/ http://drawception.com/viewgame/Kx5eLYD7w8/bruce-wayne-forgets-to-take-off-batman-costume/ http://drawception.com/viewgame/SmDXexRsK9/batman-vs-nyan-cat/ http://drawception.com/viewgame/fsQF6aFH8c/the-holy-batman-empire/ http://drawception.com/viewgame/78EMyeYge8/no-one-understands-batman/