Something that's authorized is officially approved. If the principal of your school has given you the go-ahead to throw a Hawaiian-themed party, you can call it an authorized luau.
The adjective authorized comes from the verb authorize, which means "give formal approval or sanction to." Both words go back to the Latin root auctor, "authority." So when an authority grants her approval or permission to do something, it becomes authorized. You'll need an authorized passport if you want to travel to a foreign country.