The rubber balls serve two critical functions:
They provide three degrees of freedom in the movement of the top platform relative to the bottom base. The top platform sitting on top of the rubber balls can freely move up and down, front to back, and side to side, without causing undulating, repeating motion that continues after the original vibration. They work as very effective shock absorbers.
The rubber balls are also used to balance the uneven load of some equipment such as amplifiers or turntables. By placing the rubber balls in different positions in the base, you can level the equipment to even the load.