to run: to move fast on foot, and by extension to act or travel swiftly
At its core this is the ordinary word for running on one's own feet: a person breaks into a run to greet someone, to carry news, to flee, or to charge into battle. Everything else the word does grows out of that single picture of moving fast on legs.
Because running was how messages and people were rushed from place to place before there were horses to spare, the word settled into a fixed job in the royal court. One form of it, literally "the ones running," became the standing title for the king's couriers and his armed escort, the men who ran ahead of the chariot and stood guard at the palace. Read in those passages it is less a verb than a name for a body of guards.
The same image of swift, tireless motion is then turned to figures of speech. People "run" to do evil or run the path of God's commands; the sun "runs" its course across the sky; God's word "runs" quickly through the earth; the faithful "run" and are not weary. Here running is no longer literal but stands for eager, energetic pursuit. A small group of uses are causative: to make someone run, to rush or hurry a person along, or to drive an enemy off in a chase.