Exercising on unstable surfaces, such as BOSU balls, Swiss balls, and wobble boards is a central component of many core-strengthening programs. A study from California State University, Northridge, led by James Kohler, showed that training on stable surfaces overloaded and recruited the core muscles best. They measured core muscle activation during the shoulder press performed on stable and unstable surfaces, using electromyography (measures the electrical activity of muscles).
Core muscle load decreased with the instability of the surface. Exercising on firm ground is best for overloading core muscle groups. (Journal Strength Conditioning Research, 24: 313-321)