The online dictionary gives this definition: (1) the power to determine, adjudicate, or otherwise settle issues or disputes; jurisdiction; the right to control, command, or determine; (2) a power or right delegated or given; authorization: Who has the authority to grant permission?; (3) a person or body of persons in whom authority is vested, as a governmental agency.
In addition to Stephen’s good reference of Colossians 3:17 regarding authority, I immediately think of Matthew 28:18, where the text says that Christ has “all authority” in religious matters (also see John 17:2). This means that when it comes to religious authority, I don’t have any. However, we do have the authority from Christ to “Go teach all nations” and “baptize them” by the supreme authority of the Godhead.
Brother John Moore has an excellent series of lessons regarding biblical authority: