If you are exiled from a place, you must leave and not return. Such punishment is called exile. For example, after he was removed from power, Napoleon lived in exile on the island of Elba.
The verb exile comes from the Old French word essillier, meaning “banish,” “expel,” or “drive off.” However, some people who live in exile do so happily — and voluntarily — like American citizens in exile in Paris. Don't confuse being exiled with being banned: exile is for countries. If you cause trouble at a restaurant, you might be banned from returning, not exiled.