This, similar to the ebony performance mute (see links, below) also fixes onto the bridge of the instrument to reduce its loudness. By adding mass to the bridge, it muffles the vibration of the bridge, thereby muting the instrument considerably - which your housemates/roommates will be very happy to hear! (And your downstairs neighbors will appreciate it if you also put a pillow under your endpin - that'll help reduce the transmission of sound to the floor!)
Generally speaking, rubber mutes like this are not used in performance, but rather can be most useful for reducing the volume of the instrument when practicing, by dampening bridge vibrations. Flexible, so no modifications are needed to the mute or your instrument.