You are looking at a  foam mute pad for a Rickenbacker bass guitar,this fits on the mute bar in the tailpiece. 

To fit is very easy, take your strings off, unscrew the the tailpiece, take off the mute bolts, take off the old mute pad off, clean the bar to remove any old glue and rubber/foam, take the backing off the pad and simply place firmly on the bar and refit in reverse order. Note, Make sure your earth wire is connected properly when assembling.