How brig became a naval word for prison

Is brig used to mean a prison outside the United States, and where did that usage come from?

Yes. The term comes from brigs and brig hulks being used as prison ships.

The word brig originally names a two-masted sailing vessel. Some brigs and later brig hulks served as prison ships. Their use for confinement allowed the vessel name to become a word for a naval detention space. The familiar shipboard prison term therefore preserves the name of an actual sailing type.