The Incredible Parker was Parker's alter-ego and a monsterific version of himself.
In "The Incredible Jerk," Parker was sick of all of the insults, and then, he turned into Incredible Parker and went on an insulting rampage. In the end, Parker is normal and everyone apologizes to Parker for insulting him earlier, but back at Mr. Meaty, Josh sees some heavy boxes in the freezer, and gets Parker mad so he could move them out. However, when Josh tells Incredible Parker that he needs him to lift the boxes out of the freezer, Incredible Parker responds, "No! How 'bout you clean yourself?!".