Basically, the dampener reduces vibrations in the stringbed. The debate is still out on whether they actually reduce overall frame vibrations. The lessened vibrations change the sound of the ball striking the strings. Some frames have a more tinny, ‘ping’ sound. The dampener will change that to a more satisfying ‘pop’ type sound. There is also a slight change in the feel the frame has. But again, some argue this is good, others say it’s bad.
I use a dampener because I do like the sound of the ball hitting with a dampener on. My frames are also slightly overpowered for me, and I feel that the high tension strings plus the dampener do quite a bit to kill off some of that unneeded power.
Bottom line: It doesn’t really matter. It all comes down to which feel you like better. The good thing is, they are really cheap. Try one out, and see for yourself. If you like it, then cool. If you don’t, then you haven’t wasted much money.
Source: Yahoo Answers 2009.