What is Authority?

Authority usually means the right to give orders. A sergeant has authority over the soldiers he outranks. Haile Selassie had authority over the entire nation of Ethiopia when he was emperor.

The key quality is that authority is conferred by a hierarchal system.

Such a system gives a principal/headmaster authority over students and a police officer authority over citizens.

Authority can also mean expertise and knowledge. To say “Professor Jones is an authority on seismology” is a synonym for, “He is an expert in…“

If a social hierarchy gives you the right to tell me to perform this function, then you have authority over me. In most contexts, this is the definition you are looking for.