I have one in the shed somewhere. It is a wristwatch case opening tool. You may or may not have noticed at some time that decent quality mechanical wristwatches have backs with notches round the rim, usually three, rarely four. You fit the appropriate shaped pegs in the holder and use it to unscrew the watch back. The adjustable key holders enable it to fit any size of case, firmly, to avoid the risk of scratches that various improvised methods usually cause. You should be able to find similar examples for sale now you know what it is.
