Primary: Erector spinae
Secondary: Splenius capitis, gluteus maximus, deltoid
The erector spinae muscles must withstand enduring workloads when riding a bike. For the majority of rides, these muscles will maintain a forward leaning posture. If the back becomes sore or fatigued, the erector spinae muscles are usually the culprit. The stability ball extension is particularly effective because it provides full range of motion at maximal extension. This will counter the hours spent with the back arched forward on the bike. Added weights are not needed to make this workout effective. Remember that stretching and moving muscles through their complete range of motion will help get the most out of muscle fibers.
This is an excerpt from Cycling Anatomy.