When you have power over others you are said to have dominance. For years, the British Empire had dominance over much of the world, ruling vast stretches of Africa, India, and Asia.
In packs of animals, the males will often fight to determine dominance, i.e., who is top dog. Or top lion. This happens in classrooms too, with the teacher needing to establish dominance over unruly students. If your football team has dominance over its league, it means they usually beat—or dominate—most of the other teams in the league.