The gluteal muscles are found on the posterior side of the pelvis; i.e. the butt (snigger). All mammals, including humans, have three of them layered one on top of the other. Together they work to lift your leg out to the side, rotate the thigh and straighten the leg.
The deepest and smallest of these is called (perhaps unsurprisingly) the gluteus minimus. It helps rotate the thigh medially (inwards) and adducts the leg.
Next up you have the muscle in the middle called (again, unsurprisingly) the gluteus medius. It also helps adduct and medially rotates the thigh, but also helps rotate it laterally (away from the body).
These two muscles are pretty much the same in humans as they are in other species, attaching to the same parts of the bone and fulfilling the same basic function. This is because rotation and adduction is similarly useful in humans and other animals, so there is little reason for it to change.
Things start to get interesting with the topmost muscle. Like the others it also rotates the thigh but it is also used to stabilise the upper body. This is particularly useful for a biped like us, who would be reliant on such stabilisers to stop our top half falling over all the time.
However it wouldn’t be so useful for quadrupeds who have other limbs to help stop their upper body for collapsing. As such our most superficial gluteal has a very strong incentive to become bigger and better.
The result is that the topmost gluteal is nothing special in animals. It gets the name gluteus superficialis because its most distinguishing trait is being superficial. It isn’t especially big or especially magical.
In humans, however, the same muscle has become the gluteus maximus because its just so beefy and massive. Evolution has driven it to become the largest gluteal by far.