The principle that everyone, the government most of all, is bound by known, general, public rules applied equally — a government of laws, not of men — and the contested ideal at whose center lies one distinction: a tyrant can use law as a tool over subjects (rule by law) while only the rule of law binds the ruler too.
A president loses an election and is told to leave office. He commands the army, the police, and the treasury. The law says his term is over. Nothing physically stops him from staying. Whether he goes is the whole question of the rule of law. It is the strange idea that the most powerful person in a country can be bound by words on paper, that a rule can stand above the people who could break it. Almost every government on earth now claims to honor this principle. The hard part is telling the ones that truly bind their rulers from the ones that merely use law to bind everyone else.