The BAPS, or Biomechanical Ankle Platform System, is a tool used for rehab mostly by Physical Therapists, and it is used primarily for rehab of the lower extremity.
The BAPS Board can be used for a number of rehab options, and the one that you will probably benefit the most from an exercise standpoint is to use this tool for balance and lower leg strengthening. The board allows for only certain ranges of motion based on the adaptive bottom ball that is placed under it, and it will not allow over-strenuous exercise to occur. Injured or not, that is to your benefit.
The actual board comes with resistance weights that can be screwed into it in a number of places making it a closed-chain strengthening tool as well. For those of us with poor balance, strengthening of the lower leg muscles will help to keep you from teetering all over the place. This will also benefit those with poor endurance of the lower leg muscles or any gait issues you may have.
The biggest complaint I have about this tool is the ease of use idea. There is a large learning curve that goes into this product, and unless you take the time to learn it, and do it correctly, your exercise benefits will not be as large.