It's a heat conductive sponge pad, which is wrapped around the mug before putting it in the mug press. Supposed benefits are:
1) Has significant heat capacity, so if heated up before hand, helps the mug to heat up quicker to the temperature
2) Helps get an even heat at all points on the mug
A-Pad is simply the name the US vendor gave it - dunno what it stands for

Regards