they let you change gear without closing the throttle or pulling the clutch in. so you can keep the throttle open and just kick up through the gears. it works by sensing when you kick to change gear and cuts the power to the coils for a split second so the engine unloads and can change gear.
oh you mean the thing in the picture above? thats just a connection that can pivot. if you look at your gear changer there's two of them on it.