The original wobble board is essentially a flat disc, supported on a hemisphere, and a patient stands on the disc and wobbles from side-to-side and back-and-forth. These days there are some sophisticated bits of equipment that essentially do the same thing and cost a lot more.
By standing on the wobble-board and carefully rocking in all directions, the knees re-learn their position sense or proprioception.
Proprioception is the sense of understanding without thinking exactly where your limb is and what it is doing. This is often lost after injury or surgery, and the limb finds itself in even more trouble as you stumble on the foot or land badly when stepping or jumping.