What does "exceptional" mean if not "an exception to the rule"?

To give "exceptional" meaning in a particular context, you've got to indicate which rule you're referring to. I guess it could be either "most geniuses are eccentric" or "most ordinary people are not eccentric" (which ought to go without saying, since "eccentric" means "out of the ordinary—although it has also acquired the connotation of being a bit daft).