Back when I was of a single-digit age, my own theory was that Grimace was basically a large Hershey's Kiss. It didn't really matter that McDonald's didn't sell Hershey's Kisses; it looked to me like a Hershey's Kiss, so a Hershey's Kiss it was.

I seem to recall that Grimace used to be a villain in McDonaldland, but I need to double-check this with The Big Book of the 70s when I get home from work.
later... OK, I double-checked: Grimace was indeed originally an evil member of McDonaldland, but apparently it discovered Jesus or something during a stretch in the joint, because now it's a terminally cheerful, if somewhat dim, McDonaldland drone.

I also checked out the McDonald's website, but it gave no clues to the identity of Grimace, or to the escapades of its checkered past.