You conduct heat to places such as the enclosure.
The result is that heat is removed, or dissipated from the heat generating source.
If the pad is connected to a metal plate or larger surface you have given the heat source a larger surface area by which heat can be transferred to the air and therefore increased the ability of the entire unit to dissipate heat.
Fans help bring in cool air, meaning that you push away hot air and bring in air that is capable of absorbing more heat. The fan is effectively a multiplier of surface area and achieves higher dissipation with forced air.
If the pad is not connected to anything at all then you are still potentially spreading the heat and increasing the surface area, but they function best when connected to another surface to allow heat to be conducted away. What this means is that you are potentially taking a small focused heat source and spreading it out across a larger area of the pad. It may well only double or quadruple the area (it won't be able to spread the heat across the whole pad) but in these things even relatively small increases in surface area can be the difference between 80C and 60C.
At the very least the pad gives a much better surface for you to stick a heatsink to than the plastic of the chips on the SSD. The pad will stick to the chips better than metal would. Almost any flat piece of metal would provide a good thermal reservoir for heat to be dumped in to.