Here are the mechanical requirements for a good mat:
It must have the same hardness (durometer) as the LP, so vibration from the LP can be absorbed (without reflection) and converted to heat. To this end it will affect tonality if too hard or too soft.
It must support the LP properly, at the vinyl depresses at the location of the stylus where the pressure is extreme.
It should also be effective at damping the platter! When the stylus tracks the groove, the vinyl can 'talk back' which is why it has to be controlled. But the platter can editorialize too, due to room-borne vibration. It has to be dead.
If the platter pad is working correctly, you may notice that with the volume off the stylus tracking in the groove is silent.
This is a lot to do- but the results of this are obvious- a properly designed platter pad can cause a cheap turntable to have better tonality than an expensive one. The platter pad is a critical part of LP playback!