High kicks are a flashy and dynamic part of many styles of martial arts. Though not an effective combat technique, high kicks build flexibility and strength that allow truly devastating kicks to lower-lying targets. As kenpo artist Dave Coffman says, "It's best to kick to the head once you've knocked them down."
Simple stretching is vital to being able to kick high without injury. Throwing a hard, high kick can push an inflexible person's groin out of their range of flexibility, causing a pulled or even torn muscle. Hurdler's stretches and toe touches are common stretches that will increase range of motion in the needed areas. Some yoga postures, such as Head to Knee pose, will do the same. Partner leg stretching, where one person applies pressure to increase a stretch, can be effective but should only be attempted under qualified supervision.
A stretch kick follow the same motion path as a combative kick, but uses different physics to match its intent. Where a combative kick is highly controlled, a stretch kick swings from the hip, using the foot as a pendulum. The goal for a stretch kick is to only slightly extend beyond the range of normal flexibility, thus increasing range of motion by small increments. Like other stretching techniques, a stretch kick should swing to the point of discomfort, but not to the point of pain.
Most people with kick flexibility problems have them because of lack of flexibility and control in the hip flexor muscles. For a control kick, first lift your leg to the point just before you extend at the knee. Hold your hip and upper leg in that position while you slowly extend and retract your shin and foot through the remainder of the kick. Most martial artists find it necessary, at least at first, to have a wall or partner to hold on to during this drill. Three set of 10 repetitions each will greatly increase your hip flexibility and motor control.
A final challenge interfering with the ability to throw good high kicks is strength in the hip muscles. There are many small muscles in the hip and lower abdomen that don't get used much except when executing high kicks. Lower abdominal workouts of all kinds, including abdominal crunches and side crunches, will strengthen those muscles and enable better high kicks.