Go ahead and laugh about Bosu balls and balance discs, but the reality is that they work for those of us who've suffered ankle sprains.
The most common type is a lateral/inversion sprain, in which your foot twists to the inside, stretching or tearing the ligaments on your outer shin. The telltale signs of an inversion sprain are pain, swelling, and eventually discoloration on the outside of the ankle.
Your peroneals — muscles on the outside of your shin — are in charge of preventing inversion. If they're working properly, they'll contract fast enough and powerfully enough to straighten the foot before the ankle rolls and your ligaments stretch or tear.
Once you've suffered an ankle sprain, you're going to have functional ankle instability unless you follow a good rehabilitation program. In this area, the research has shown over and over again that training on unstable surfaces — wobble boards, Bosu balls, balance discs — can correct this proprioceptive delay and get rid of functional ankle instability.
That's why unstable surface training is a great rehabilitation tool. This doesn't mean the same techniques can, or should, be used with healthy athletes to prevent ankle sprains, improve balance, or enhance performance. In fact, if instable surface training were to take the place of something else in their training plan, it usually makes things worse.