rule or dominion: the authority to govern, and the realm over which it is exercised
The word names two things at once: the act of ruling and the territory or sphere that ruling covers. It answers the question "who is in charge here, and how far does their control reach." The same word can describe a king's realm, the sun's turn over the daytime sky, and God's rule over everything he has made.
What sets it apart from plain words for power is that the authority is granted, held on behalf of someone higher. In the creation account the sun and moon do not own the day and the night; they are appointed to govern them, the way an official is given a post. That flavor of assigned office, rather than raw force, runs through most uses.
How far the authority reaches, and how long it lasts, depends entirely on who holds it. The rule of a human king (Solomon's, Hezekiah's, Babylon's) is bounded by a border and ends with a reign. God's rule is described as covering "all places" and lasting "throughout every generation." Over time Hebrew writers leaned on this word more and more for that everlasting divine rule, until it stood side by side with the ordinary word for kingship, מלכות.