To govern is to rule, lead, oversee, or otherwise control. Each U.S. state has its own governor, whose job it is to govern the affairs of that state.
While it's true that governors govern — that is, they head the executive branch of their state government — there are lots of other ways to use the verb govern. Almost anything that controls or has a lot of influence over something else can be said to govern. The rules of tennis, for example, govern the way that game is played. In mechanics, a device that controls other devices is called a governor. My dog's basic needs govern the way my household is run: his schedule is our schedule.