This article contains plot details from the latest book.
“Whoever decided we should wear capes was an idiot.”
Capes are a form of Elvin status. When in the Nobility, a cape is often worn. At Foxfire, short half capes are worn to show that prodigies go to a noble school. While elves of Nobility don't have to wear capes, even to formal occasions, but it is highly recommended. It was mentioned in Book 1: Keeper of the Lost Cities, while Sophie was going to bottle Everblaze that capes actually provided useful as a smoke filter.
Capes are often clasped with a family crest pin.