When my uncle (he's a contractor) lays down ceramic flooring, he uses this deliciously springy subflooring (padding) between the wood or cement floor and the ceramic tiles. It is bouncy enough that we used to flop on it when we were kids tagging along on jobs. They even use it when doing heated ceramic floors.
The padding has the same effect in both cases, it dampens. With the toys, it absorbs and diffuses vibrations; with the flooring, it absorbs the impact of people walking on the tiles.
Sorry... my, ermmm, blue collar is showing