Overhead light fills a room. A wall sconce does something different: it puts light on the wall, low and to the side, softer and warmer than anything hanging from the ceiling. The sconce is one of the oldest lighting forms there is, and it survived every change in the technology because the job it does never went away.
The form goes back to the candle and the torch, a bracket on the wall holding a flame. Gas lighting kept it: the gas wall bracket, swinging out on its pipe, lit halls and stairs across the Victorian era. Electricity kept it again, and the electric sconce carried the vocabulary of each style that followed, ornate and cast in the Victorian house, geometric in the Deco apartment, spare in the mid-century room. Through all of it, the sconce did the same thing: light at eye level or below, thrown against a wall. That placement is the whole point. A sconce lights the vertical surfaces of a room and bounces a soft glow back, which flatters a space in a way downlight can't. It fills the gaps overhead fixtures leave, a hallway, a stair, either side of a mirror or a mantel.
Salvager's Note: Sconces were usually installed in symmetrical pairs, so a matched pair is worth considerably more than a single, and the mate to a lone sconce is one of the harder matching problems. If you need two, buy the pair together.