Supercilious people think very highly of themselves, more highly than of others. If your sister tends to act snobby and superior, you can describe her as supercilious.
You might expect Nobel Prize winners to be supercilious — after all, they've reached the very heights of their profession. But one-on-one, your famous physics professor might be humble and fun to talk to, anything but supercilious. Most often, it's people who have no right to be arrogant, rude, and holier-than-thou who behave in the most supercilious ways. The Latin root supercilium means "haughty demeanor," but also "eyebrow" — as in an eyebrow raised in a haughty, supercilious expression.