IIRC, and my books are currently packed up so I can't check, depravity was a mechanic from Heroes of Horror. It was meant to emulate the physical and mental corruption that truly evil situations can impose. I remember there were various benefits and penalties that it would imbue as your score went up, but it always struck me as also being really random (ie you would hit a new score, then roll on a chart to see the effect. It could easily turn your character unplayable.)
Anyway, I'd ignore all of that for a 4e game, especially for a new dm. It varies wildly from the default assumptions of the game and could easily turn everything unfun.