What happens there that makes the area past the "overdrive" point more prone to clipping or distortion?

Part of the reason that I am curious is because once in a while I crave a little more volume than the "0 db" level. I mean, I'm not overly worried as it still sounds fine to me, but I was wondering what exactly was happening when I ventured into the overdrive zone. If I knew then perhaps I would be able to shake the strange paranoia I get when I'm "in the red".