to throw or shoot something out: cast a stone, hurl down, shoot an arrow
This is the plain, physical sense of the word: to send something out of the hand. It covers throwing a stone at someone, hurling a thing down so it loses its standing, and shooting arrows at a target.
It is rare in the Bible, surviving in only a handful of places, and it is almost certainly the older, concrete root behind the far more common worship word. Many scholars connect the two by the picture of the hand: thanksgiving and confession were marked by raised or extended hands, and the same word that meant throwing the hand out came to mean acknowledging God or one's sin out loud. Whether or not that link is exact, in the worship passages the physical action has dropped away entirely, so the two are best treated as separate words.