a king: the single supreme ruler at the head of a people, city, or land
A king is the one ruler who holds the highest authority over a people or territory, normally for life and normally passing the throne to his son. The same word covers a huge range of power: it names the ruler of a single Canaanite town, the head of a small tribal people, and the emperor of a world power like Egypt, Assyria, or Babylon. So a biblical king is not always the grand figure the English word suggests; often he is simply whoever rules a given place.
This is the ordinary, everyday word for that office, and most of the time it carries no praise or blame in itself. It is used freely of Israel's enemies and of the great empires, where the king can be opposed, defeated, or judged, just as much as it is used of David or Solomon. What changes is not the word but the people it describes.
In Israel the king was meant to rule under God, not in God's place. The people's demand for a king "like all the nations" was treated as a turning away from the LORD's own rule, and from then on each king was measured by whether he kept faith with God. The same office that other peoples simply took for granted became, in Israel, a thing argued over, hoped for, and feared.
Out of that tension the Bible takes a further step and calls the LORD himself the true King, the one who really reigns over Israel and over the whole earth. Every human king, Israelite or foreign, is then answerable to this higher throne, and the prophets and psalms increasingly look past any human ruler to God's own kingship.