J.V.
Pilates is a training program developed by a guy named Pilates! Most of the early practitioners were dancers. The basic idea is to build strong, flexible, lean muscle, so a lot of the work focuses on "the core."
There usually isn't much equipment, as the body itself is used to provide its own resistance.
Yes, Pilates can be done anywhere! I do it almost every morning in my family room. I usually combine it with yoga, as breathing and stress relief is also a major part of Pilates.