"Authority" is the quality of being in control of things. A boss has authority over his or her employees. Parents have authority over their children. And people who are experts on a topic are sometime called "an authority on ___":

Gantz is a leading authority on Native American history and culture.

The word "authority" is used in several common phrases, including:

• to respect (someone's) authority
• a position of authority
• authority figures (people who have authority)
• have legal authority