There are basically two schools of though on this. 1) Decoupling the record from the platter, 2) dampening the record vibrations which usually involves the dampening of the record and stronger coupling to the platter. the former is mostly to prevent platter vibrations from affecting the record and playback. The latter to dampen the record vibrations caused by the needle tracking the record.
something like the Ringmat supports decoupling. but unless the platter is excessively resoanant, I find this to brighten the playback elevating the mids/treble to almost the point of brightness. Bass is reduced also.
On the other hand, dampening mats (Millenium, boston audio, copper, etc) tend to act like tone controls. while they perform better overall in my opinion, the trick is to find one that has a flat frequency response but provides all of the benefits of dampening. so far, a good copper platter coupled to the platter (like the TW acustic) or a leather mat perform the best. I have tried Millenium and Boston Audio. I think leather mats are highly cost effective and are pretty neutral.
Andrew