Isometric contractions as exercise have some positive and negative qualities. Stabilizing muscles generally contract isometrically, while the prime movers contract isotonically (concentric and eccentric combined). In most motions you will have both stabilizers and prime movers activated at the same time. Training for specificity is important for sports/activities, in other words practice the motions you need for your sport. Specific isolated isometrics are rarely needed for sport, however they can be useful for stabilizing muscle groups like the abdominals. Yoga is one of the few isometric exercise examples and that only covers a portion of yoga.
Training isometrically means to hold a position while the muscle length and joint angle do not change. This is will mostly benefit the position you hold, and not the entire range of motion. We live dynamically so why train/exercise statically? The main reason to perform isometric exercises would be rehabilitation. By maintaining a joint angle there is less risk for re-injury to the damaged joint and/or muscle. Muscles and joints do not have the same strength throughout their ranges of motion, so it is best to start the rehabilitation process within a safe range where both are strong. As mobility and strength return it is important to reintroduce motion.
When you have an acute injury see your health professional for acute care and advice on rehabilitation, you could very well be prescribed isometrics to start.
Dr. Nelson