The hyper extension exercise on a stability ball is a workout that involves using a stability ball to perform a back extension exercise. To perform the exercise, you would start by lying face down on the stability ball with your feet on the ground and your arms extended in front of you. Then, you would use your back and core muscles to raise your upper body up off the ball, keeping your arms straight and your head in line with your spine. 

As you extend your upper body, you should feel your lower back muscles engage and stretch. You can hold this position for a few seconds and then slowly lower your body back down to the starting position. This exercise can be repeated for a certain number of repetitions or for a set amount of time.

 Some potential health benefits of performing the hyper extension exercise on a stability ball include improved core stability and lower back strength, increased flexibility in the lower back and hips, and improved posture.