Hi Angie. Actually a ball is not involved in the basic 34 mat Pilates moves. The poses are floor poses and you need a mat.
There are variations of Pilates that are fun but not necessairly based on the Pilates principles. There are exercises such as:
"Pilats on the Ball"; "Yogalates"; weight training with Pilates" and more.
All of the principle poses are designed to strengthing the core giving you more stability, toning, and strength. Below are two articles I have written on Pilates. Maybe you will want to try a beginners Pilates class. Thanks for posting.Introduction to Pilates Principles Your Core Source of Strength and Stability