A treasury is a kind of bank — it's a place where money and other valuable things are kept, or where a country keeps its wealth.
You might guess that a treasury is a place to keep your treasure, and you'd be right. Originally, the word literally meant "room for treasure," from the Old French tresor, "hoard or treasure." Starting in the late 1300s, it also meant "department that controls public revenue," which remains the most common use of treasury today. The U.S. even has an official Department of the Treasury, the part of the executive branch that prints money and collects taxes.