Pilates is a physical training method, to increase strenght, flexibility and control of the body. It is a mix between dance, yoga and gymnastic, and it can be done on a floor mat or with apparatus. According to Wikipedia, this method seek to develop controlled movement from a strong core and it does this using a range of apparatuses to guide and train the body.
Strong core muscle, is the basis for a strong back, especially the low back. Most of the low back pain will be relief from core exercise, and better posture will be notice. Two excellents methods to reinforce the core muscle are the swiss ball exercise or the pilates classes. There is multiple video and book on the method, but I suggest that you first take a class to learn the good technique, because you can hurt yourself if the methods is not done properly.
Related article: Strong back and good posture with core muscle exercise.