Pilates is a system of exercises that include certain principles such as coordination, centering, control, precision, flow and breath. Everything in Pilates is a mind-body connection, just like in yoga, but Pilates specifically focuses on the 'powerhouse,' a group of muscles, that work together to create stability for the hips and spine so you can function in the most elevated way.
Pilates was established in the early 1900's by Joseph Pilates of Germany. It used to be called Contrology until Joseph's passing.
Here are a few short videos if you'd like to learn more: