The left trap is set using the metal key which flips over to hold the top spring down with the noose in the hole. Inside each hole a spike is baited with food which when moved triggers the trap.
The right trap is a similar principal but is set using cotton which is wound through the trap (see slits underneath and tied off at the front. The mouse has to put it's head through the noose and bite the cotton to get to the bait. This though releases the sprung noose.