Good coordination with regard to a certain movement can be defined as the right muscles tensing the right amount at the right time. Most people trying to improve their movement ability for sports will therefore spend time lifting weights to train their ability to quickly and forcefully contract their muscles.
That is a fine idea, but it sometimes ignores the equally important flip side of the coordination coin. If coordination means all the right muscles firing at the right time, this also means that any muscles not involved in the movement must relax in the right places at the right speed at the right time. Therefore, any act of coordination requires the skill of relaxing the muscles that aren’t essential to the movement. If the non-essential muscles aren’t relaxed, they will cause extraneous movement or tension that interferes in the desired movement and wastes energy.
The zen of piano
Imagine a pianist playing the piano. Each time she strikes a key with a certain finger, the other fingers must be relaxed so the wrong key isn’t struck at the same time. So, the skill of relaxation is an essential component of playing. If you want to get a little zen about it, you could say that the non-doing is just as important as the doing.
The pianist's skill is an example of differentiated movement – the ability to move one segment of the body while keeping a nearby segment still. Belly dancers have excellent differentiated movement - they can isolate small movements in their torso and hips while keeping other areas still or even moving them in the opposite direction. By contrast, most Americans, especially white male Americans, tend to move their hips and low back as one big block. This generally leads to poor performance in dancing, and is partly caused by insufficient skill in relaxation.
The key to sprinting
Quick and accurate relaxation is also essential to good sports performance. Take the example of a sprinter. Elite sprinters have an unusual ability to maximally contract their muscles very quickly. But research shows that they are even more unusual in their ability to quickly relax their muscles. Why is the skill of relaxation important to sprinting? The simple reason is that any muscle that contracts to push a sprinter forward will in the next phase of the gait cycle be asked to lengthen. If the muscle is slow to lengthen, it essentially put the brakes on forward movement. Here's a quote from famous sprint coach Charlie Francis:
the number one secret to greater speed is relaxation! It allows a faster and more complete shutdown of antagonists, quickening alternation cycles and permitting more force to be delivered in the desired direction with less energy consumption. Relaxation must become second nature in every drill you do and every run you take. You may feel that you aren't generating enough force while relaxed (a perception that gets a lot of sprinters into trouble in big races), but remember, only the net force counts! The net force is the amount of force delivered in the desired direction minus the force generated by the antagonist muscle at the same moment.
Golfers, tennis players, and baseball pitchers would give similar advice about executing maximum power. This is why any great athlete makes it look easy, and has the ability to generate enormous power even while looking very relaxed and smooth.
Relaxation skill is also important to prevent excess muscular tension in everyday life. A person working at a computer needs to move only his fingers and wrists. However, the stress of the work will often cause what Moshe Feldenkrais called parasitic tension - unwanted and unnecessary muscle contraction in many other areas, e.g. theshoulders, neck, or jaw. The ability to keep these muscles relaxed while typing is a skill, and can be developed like any other skill.
Despite the importance of relaxation in physical comfort and performance, most people never think to train it, instead favoring exercises that develop the ability to contract muscles. Some good methods to train relaxation during movement or posture would be the Feldenkrais Method, Z-Health, Alexander Technique, or tai chi. These methods use slow movement to ensure that muscular effort happens with the greatest amount of differentiation, ease and smoothness, and the least possible amount of effort and strain.
Taking off the parking brake
To sum up, consider the analogy of a car. Imagine trying to drive faster with a foot that is so clumsy that it steps on the brake every time it steps on the gas. Not only will you not get anywhere very fast, you will tear up your car in the process. It takes the skill of relaxation and differentiation to ensure that you when you step on the gas you do not also step on the brake. So, next time you train, think about whether time is better spent by flooring it or learning to keep your foot off the brake.