The vibrating shoes were developed by Dr. Richard D. Koenig a podiatrist from St Louis. The Doctor’s website explain in detail how you can order the shoes, how modern their design is and how comfortable they are, but actually very little information is given regarding the supposed benefits of using them.
According to Dr. Koenig’s site "Research gathered in the last five years and outlined in The Lancet medical journal, found that elderly people showed signs of better balance when they stood on a pair of battery-operated randomly vibrating insoles. The idea is that the vibrations amplify balance-related signals between the feet and the brain that become dulled with age or illness. Young people who need extra help with balance, such as construction workers, gymnasts, acrobats or other athletes may also benefit from the vibrating signals".
More information on the floor which uses vibrations can be found here.