Pilates is a type of physical fitness system developed about 100 years ago in Germany.
The program focuses on core postural muscles which help keep the body balanced and are essential to providing support for the spine. This includes teaching awareness of one's breath and spinal alignment. The goal is strengthen deep torso muscles.
The group of muscles in the center of the body (the "powerhouse") is comprised of your abdomen, hips, buttocks and lower back. This is not significantly different from what more modern fitness instructors refer to as the "core".
Control, precision, flexibility and efficient movements are all a part of Pilates. There are to be no uncontrolled or sloppy movements.
Pilates uses a number of pieces of equipment, including the "magic circle", arcs, light weights and mats. Other devices include the "ladder barrel", "Wunda chair" and "Trapeze table". Large balls, resistance bands and foam rollers may also be used.
Be aware that the term Pilates has been declared to be a generic term, so anyone can claim to be an instructor. This method of exercise would certainly benefit from some form of a recognized and respected instructor certification program.
Here's a place in Boston where you can try Pilates.