We've been doing some intensive matwork recently in Ballet Sculpt, focusing on the glute medius which is positioned to the outside, upper part of the glutes (the butt, backside, you get the idea...)
We also rely on the gluteus medius when balancing on one leg - not stretching and allowing it to feel "tight", can lead to back pain and pain when walking.

It is less robust than the big muscle at the back and fatigues easier. It isn't the easiest muscle to target and stretch easily, so take the time to hold these stretches for 40 - 60 seconds.

Do these stretches when you're warm - after a workout or a walk, when your muscles are pliable and you're not risking strain. If you feel any pain, stop! Discomfort is different - grit your teeth!

There are two trigger points for the glute medius - pressing them and massaging into these areas can relieve tension and pain in the back and glutes. Try holding for 10 seconds, releasing and repeating as necessary!