If by some kind of mistake you're suspended from the College, ie. you kill a companion, this quest starts. Speak to Tolfdir and you must pay 250 gold for your first offense, 500 gold for the second, and 1,000 gold for every subsequent offense. This is if you committed a serious crime. If you struck a college member or pick-pocketed one of them, you won't have to pay. That's it. Pay up!