This is an STS... it stands for Shock Terminator Suppression... which is an overly complicated way of saying it helps eliminate shock, noise and vibration on the shot.
The way it works is just like plucking a guitar string and then pressing your finger on the vibrating chord.
This is a limbsaver, installed on a solid limb bow. Vibration is the #1 enemy of a compound bow... or any bow for that matter. Vibration always tends to occur the most, or be drawn to, extremeties... additionally, rubber helps soak up vibration through movement... having these stick on limbsavers on your limbs will help eliminate both noise and vibration... which is really just wasted energy that did not transfer to your arrow.