An adverb meaning something happened to a great extent. If somebody (verb)ed the shit out of (object), it means that person REALLY (verb)ed that (object) hardcore.
> The Tampa Bay Devil Rays beat the shit out of the New York Yankees last night. The score was 15-2!
> [Rachael Ray] really baked the shit out of that pie. That [motherfucker] was tasty as hell!
> [Haley Joel Osment] really saw the shit out of those dead people in "The Sixth Sense."
> [Rosie O'Donnell] devoured the shit out of that two-pound burger, then proceeded to wolf down an entire cheesecake.