Every time we move we use several specific areas of our brain. The brain then sends an impulse through the spinal cord to muscle fibers. When you learn to voluntary engage certain muscles (like deep core activation in Pilates) you fire a movement chain that might have been asleep for a long time.
A healthy nervous system means better communication between your brain and other parts of your body as well as the release of stress-fighting and mood-boosting hormones.
You have probably heard a lot about the benefits of mindfulness for your mind and body. To sum them up: