Just like it says, this is the combat arena. Pit-styled and surrounded by bleachers, if you've got a problem with someone what better way is there to settle your differences than punching the hate out of each other? And if your fellow fortress dwellers are placing bets on who goes down first, who are you to disappoint?
This area is also used for sport, whether it be the torture of a captured non-infected, or the beating of a prisoner. Even tournaments are held here.
