Exercise balls were not invented by Joseph Pilates but they are commonly used in Pilates routines.
The main benefit they bring to Pilates is the instability they give the core. That instability means your core is more tested. As with other Pilates accessories they are relatively inexpensive but help you adapt Pilates exercises to make then different and also harder.
There are numerous ways you can use the exercise ball in a Pilates workout. Fairly easy moves include the pelvic curl and spine stretch. More advanced moves include the roll up where you hold the fitness ball in your hands and the open leg rocker where you position the ball between your ankles. So the ball will provide a leverage challenge to some exercises and instability to others.
Make sure the ball is burst resistant. This is really important if you are using the ball to support your weight for any type of exercise. If it gets damaged, the ball should then slowly deflate and not burst causing you to become injured. They should therefore have a weight limit.
Look at the different sizes, your height should determine the size you buy.
If you are between 5ft 1" and 5ft 7" the ball should be around 55cm for example. When you have purchased make sure you keep it fully inflated.
Seems obvious, but with prices for an exercise ball ranging from £9 through to £225 for a Technogym Wellness Ball, price shoudl be something you consider before you just pay out.