He was a really bad governor and woefully out of his depth, profoundly under-qualified. He only lucked into the job by a quirk, when Californians recalled Gray Davis for what never should have been a "recall-able offense," and later was uncovered to be something that wasn't remotely his fault, as blocks of power sales had been illegally manipulated by companies like Enron. As a result, Mr. Schwarzenegger didn't really have to run for governor, but could just sort of put his name out there, not go through a serious campaign, and only participate in one, especially-easy big group debate. Wouldn't it be cool, enough Californians must have thought, to have the Governator running the state. No, it turned out, it wouldn't be. It was a job that actually required someone who had a clue what he was doing.
It does speak volumes, though, when as soon as he was out of office his first thought was not to show any seriousness in other avenues of politics or public service, but to run back to Hollywood where he could blow things up, blow 'em up real good.