Someone who's highfalutin thinks they're much fancier than other people. Your highfalutin cousin likes to sound impressive by using words like perspicacious and abnegation, though she doesn't really know what they mean.
The U.S. slang term highfalutin was coined around 1840, possibly from high-flying or the Yiddish hifelufelem, "nonsense." It's an appropriately folksy word to use when poking fun at people who put on airs. Your highfalutin classmate might constantly quote Shakespeare, show off his expensive new watch, refer often to his travels abroad, and generally act pretentious and condescending toward everyone else.