A garret is a room at the very top of a house, just underneath the roof. If you don't have enough money to rent a proper room, you might be able to rent a garret.
Garret comes from the old French word guerite, which means "watchtower" or "sentry box." These days, a garret has nothing to do with war; it simply means the little room at the very top of a building, which is also called an attic. The idea of living in a garret is romantically associated with being a starving artist — great if you don't mind hunger and stooping over all the time because the roof is so low.