So this idea that instability training is better then training on a flat service is absolutely rubbish. There have been numerous studies that have proven the ineffectiveness of it compared to flat stable surfaces. If your trainer or anyone for that matter tells you training on a bosu ball gives you better core strength, just simply tell them, you trolling? No, only joking! Just simply tell them it is not as much effective then training on a flat surface.
Instability training has been extremely popular among bodybuilders and power athletes for more than 10 years. The theory behind the method is that training on unstable surfaces such as bosu balls or swiss balls for that matter, forces muscles to stabilize the body to perform the exercise, which requires additional muscle activation. Few studies support this. A Norwegian study measured muscle activation in the upper body and core muscles during a 6-rep maximum bench press performed on stable and unstable surfaces. Muscle activation when training on unstable surfaces, as measured by electromyography, was a lower for every muscle group. In fact, activation of the rectus abdominis was more than 30 percent less when training on the Swiss ball or balance cushion than on a stable surface. Instability training is less effective than traditional training for building strength in prime moves or trunk-stabilizing muscle groups. (Journal Strength Conditioning Research, 27: 1101-1107, 2013)