Its meaning is made a bit clearer by Principal Skinner at one point: (If anyone can remember the episode, let me know.)
"He embiggened that role with his cromulent performance."
Now, one meaning of "embiggen" is "to make nobler", or "to make better". That's the meaning used here, and for a role to be made better by the performer, then that performer must be very good actor -- a legitimate professional actor, if you will.
"Cromulent" doesn't have a direct equivalent elsewhere in English, but from the uses it has on the Simpsons, my guess is that it means something between "legitimate" and "good."
Jurph suggests "accurate" or "realistic", which seem to fit in well.
mr100percent adds that he thinks the word first appears in Treehouse of Horror V.