The gluteus medius muscle is located in the upper part of the glutes, just below the hip bone (iliac crest). The gluteus medius muscle is very important in stabilizing our hips during exercise or sport. It is weak in most people and this weakness can be a major source of problems in the lower back, SI joints and IT band. Running or jogging can reveal long hidden weakness in this muscle, but you don’t have to be an athlete to have gluteus medius problems. Because simply standing, walking, or sitting requires participation of the gluteus muscle, clients that lead mostly sedentary lifestyles often develop weakness here that leads to different pain syndromes.
Here is an interesting article and another explaining the importance of the gluteus medius muscle as well as some exercises to help strengthen it.