to set something down in a chosen place: to put, station, or present it there deliberately
This verb is always about deliberate positioning. Someone takes a thing, or a person, and sets it in a particular spot on purpose: peeled rods in the watering troughs, a fleece on the threshing floor, the ark beside an idol, five brothers before Pharaoh. It is not the loose word for putting anything anywhere; it pictures a purposeful placing where the spot matters.
From that concrete core the word reaches in a few natural directions. It can mean bringing a person forward and standing them before someone of higher rank, closer to "present" than to "put." It can turn figurative, setting a person into a condition: God sets the sufferer up as a public byword, or leaves a woman as exposed as the day she was born. In one prophetic call it means to fix something abstract firmly in place, to establish justice in the town square. And in its one passive use it flips to the receiving end: to be left behind, held back.
Throughout, the word stays close to the idea of causing something to stand in position. It is a near neighbor of the more common verb for stationing something upright (נצב) and a narrower, more deliberate cousin of the all-purpose word for putting or placing (שׂום).