Fitness ball

A Fitness ball is a ball constructed of elastic rubber with a diameter of around 60 – 80 cm. It is used in physical therapy and exercise.
Using a Swiss ball as part of a fitness program can include a wide range of difficulty levels, each requiring support from the back and stomach muscles that help firm up the trunk muscles in the body.
Some people sit on a Swiss ball instead of a chair (for example, an office chair), since this position requires them to engage their abdominal and back muscles and maintain proper posture to remain balanced on the ball.
Learn how to use this popular fitness tool for a wide variety of exercises. Watch this video: Stability Ball.

Fitness ball – improving proprioception
The proprioceptive sense is believed to be composed of information from sensory neurons located in the inner ear (motion and orientation) and in the stretch receptors located in the muscles and the joint-supporting ligaments (stance). There are specific nerve receptors for this form of perception, just as there are specific receptors for pressure, light, temperature, sound, and other sensory experiences, known as adequate stimuli receptors.
Although it was known that finger kinesthesia relies on skin sensation, recent research has found that kinesthesia-based haptic perception strongly relies on the forces experienced during touch. This research allows the creation of “virtual”, illusory haptic shapes with different perceived qualities

Fitness ball and Physical therapy
Physical therapy is the provision of services to people and populations to develop, maintain and restore maximum movement and functional ability throughout the lifespan. It includes the provision of services in circumstances where movement and function are threatened by the process of aging or that of injury or disease. The method of physical therapy sees full and functional movement as at the heart of what it means to be healthy.

Fitness ball and Sensory-motor coordination
Integration of the sensory perception and motor output occurs in the cerebellum. The cerebellum is linked by many neural pathways with the motor cortex—which sends information to the muscles causing them to move—and the spinocerebellar tract—which provides feedback on the position of the body in space (proprioception). The cerebellum integrates these pathways, using the constant feedback on body position to fine-tune motor movements.

Fitness ball and pilates
The Pilates Method is a physical fitness system that was developed in the early 20th century by Joseph Pilates. Pilates wrote at least two books about the Pilates method: Return to Life through Contrology and Your Health: A Corrective System of Exercising That Revolutionizes the Entire Field of Physical Education.
Pilates called his method Contrology, which refers to the way the method encourages the use of the mind to control the muscles. The program focuses on the core postural muscles that help keep the body balanced and are essential to providing support for the spine. In particular, Pilates exercises teach awareness of breath and alignment of the spine, and strengthen the deep torso muscles, which are important to help alleviate and prevent back pain.

(some from wikipedia)