Gluteus Medius is an upper buttock muscle. Gluteus Medius is many things - a pelvis stabilizer, a hip abductor, a running muscle, a lifting muscle, and also a muscle that can cause a great deal of pain.
Gluteus Medius Anatomy
Gluteus Medius, pictured above, lies in the upper buttock region of the body. Gluteus Medius lies on top of its associate Gluteus Minimus, and above its better known buddy Gluteus Maximus. Gluteus Medius connects from the top of the femur to the Iliac Crest (back of hip/pelvis bone), and is a wide, fan shaped muscle. Unlike many muscles, which are thin and bulb-like similar to hydraulic pumps, Gluteus Medius spans a fairly large surface area.
Gluteus Medius Function
Gluteus Medius functions in isolation as a hip abductor. Hip abduction is the act of lifting the leg away from the body, as shown in the image below. Hip abduction is also critical in keeping you upright when standing on one leg - especially in physical activities like running. A hint to feel Gluteus Medius working while standing on one leg: when standing on your right leg, your right Gluteus Medius fires to prevent you from falling over to the left.
Hip Abduction - A Function Of Gluteus Medius
Gluteus Medius also has secondary functions in stabilizing the pelvis and lifting objects. When carrying a heavy load, for example, Gluteus Medius (along with the QL muscle) works hard to keep the pelvis in a safe position and protect the lower back. Gluteus Medius will help stiffen and stabilize the body when strength is required. In addition, Gluteus Medius will activate when lifting objects off the floor. It is during activities that require great effort from Gluteus Medius - lifting a heavy object, playing basketball for the first time in years, or carrying a heavy load - that Gluteus Medius is subject to strain, knotting, and trigger points, which all manifest in the body as pain and tightness .
Gluteus Medius Pain
*Rant* In my experience, nearly everybody has Gluteus Medius pain in some capacity. The main reason for this is our increasingly sedentary lifestyles. Sitting all day typically won't directly bother the Gluteus Medius, but it will atrophy the muscle to the point where any physical activity will trigger strain, knotting, and Gluteus Medius pain. Once Gluteus Medius pain is present, it can feel worse while just standing or sitting for too long. We need to properly release and strengthen the Gluteus Medius muscle to make it the powerful force it is meant to be, and get out the chair more often. *End Rant*
The Gluteus Medius pain pattern below is depicted by Travell & Simons work on Myofascial trigger points and pain in the body . The bright red areas illustrate where pain caused by Gluteus Medius can be felt, and as you can see the pattern is quite gnarly.
Gluteus Medius Pain Pattern 
Gluteus Medius Release
When using a muscle release/massage therapy school of thought for lower back pain relief, Gluteus Medius should be high on the list of muscles to work. Effective Gluteus Medius release will destroy any knots, trigger points, and tightness contributing to the nasty pain pattern above. Gluteus Medius release can restore the natural, healthy inward curve to the lumbar spine, and relieve a lot of pressure off the lower back. Release of the Gluteus Medius muscle can be done by the hands of a professional physical or massage therapist, or using an at home massage tool like QL Claw.
QL Claw is great because it was designed to release every muscle that contributes to lower back pain when tight - and Gluteus Medius is high on that list. Check out the Gluteus Medius release tutorial using QL Claw:
Gluteus Medius Strengthening
After thorough release of the Gluteus Medius muscle (this can take 5-15 massage sessions), it can be beneficial to strengthen Gluteus Medius to prevent falling into pain in the future. In addition, Gluteus Medius strengthening exercises are very functional and have great carryover to physical sports. It is important to release Gluteus Medius first, because strengthening will not eliminate the painful constant muscle tension.
Check out the articles at the links below from some great Gluteus Medius strengthening exercises!
 Davies, Clair, and Amber Davies. The Trigger Point Therapy Workbook: Your Self-Treatment Guide for Pain Relief. 3rd ed., New Harbinger Publications, Inc., 2013.
 Donnelly, Joseph M. Travell, Simons & Simons Myofascial Pain and Dysfunction: the Trigger Point Manual. 3rd ed., Wolters Kluwer Health, 2019.