Authorization is an official form of approval for something. You'll probably need to get authorization from the owner of a coffee shop before you hang your oil paintings on the walls.
People in control are known as authorities, and their official okay, or authorization, gives you the ability to do something. The authorization of a loan means the bank grants the loan. Authorization can also refer to someone's power — if you are able to fire people, you have the authorization to do so. At the root of authorization is the verb authorize, which comes from the Latin auctor, "master or leader," or "one who causes to grow."