Meditation for your mental training can improve your level of focus, concentration, and appreciation for your exercises. Yet, moving meditation adds another element altogether. There are many different methods of moving meditation, but they all have similar benefits if your mental focus and breathing proficiency is there. Moving meditation is useful whenever you're in need of a full relaxation, or even recovery from a workout.
What is art? I see the human body and its structural movements as an art form of the highest degree. Moving meditation can add some context, tranquility, culture and honor to that art. Tai Chi, Baguazhang, Xinyiba and other internal martial arts are a great way to do so, and become healthier, stronger, and more flexible. Yoga is another way to do so from a different perspective and culture. All types of moving meditation should be executed with full concentration. Your every movement will be a part of your meditation; a sloppy movement with weak intentions means a sloppy meditation with weak results.
The more you perform your moving meditations, the more relaxed your body can become. Learning to relax and quiet the body is just as important as learning to contract it and use full force. Relaxing the body will allow you to achieve the same for your mind. It's a great way to encourage a smooth, healthy blood flow on rest or recovery days, which can speed up your recovery from a workout and reduce stress. Also, because it's so great at moving energy and waste through and out the body, moving meditation is great for managing illnesses as well.