Supercilious people think very highly of themselves, more highly than of others. Think of them as a "super silly ass," and you'll remember the basic sense of supercilious.
You might expect Nobel Prize winners to be supercilious. After all, they've reached the very heights of their profession. But Dagmar was incredibly humble and fun to talk to: she was anything but a "super silly ass." Most often, it's people who have no right to be arrogant, rude, and holier-than-thou who behave in the most supercilious way. It's the people who really are exceptional who don't feel the need to behave superciliously, because they've got nothing to prove. Most supercilious people are just insecure.