The glutes make you move fast. Especially forward and laterally.
They also seem to be eye catching.
And according to the discover channel women prefer men w/ a nicer set of glutes as well (sorry could not find the study online). But this would make sense that through millions of years of evolution it is in our very nature to be attracted to traits linked to survival, like strength, speed and intelligence. Just saying, a guy w/ a big ass is probably going to be faster and stronger.
Could this give rise to saying "His brains are in his butt"? I wish, but I highly doubt it.
The hip flexors produce knee drive which is what it sounds like, driving your knee fwd to increase stride length and move faster.
This picture may help a bit more. They pick up your leg so you can move it fwd, a job often given credit to the quads......nnnnnot totally true, but the rectus femoris does flex the hip up to around 30 degrees so I guess you could say "kinda"....
The hamstrings help the glutes make you move fast, as well as keep your knee where it should be.
They're also one of the most blamed muscles for injuries in athletes when it's really not all their fault. Typically if the hip flexors wouldn't have been so tight, pulling the pelvis into anterior tilt, putting the hamstring in a tight elongated position and compromising the glutes ability to extend the hip the hamstring would've been just fine.
The quads help you decelerate and also help keep your knee from doing abnormal things. I should mention that although deceleration is extremely underrated it still doesn't justify direct, isolated quad work.
On a side note they are also the culprit of "thunder thighs". Not to get all body builder on you however the glutes grow posteriorly, and so do the hamstrings for the most part, but the quads grow the whole way around. So there's another reason to hate leg extensions, besides that they are worthless.
BTW you should've seen some of the pictures I just saw looking up that quad. Gross, ridiculous, and hilarious, like I'm laughing at you not w/ you kind of hilarious, all rolled into one).
The calves help us absorb initial force and vice versa promote turnover and propulsion during running and jumping. It's also the place of my favorite name of any muscle in the body (but not favorite muscle): The Gastrocnemius.
W/o these we'd be bouncing around a lot more.
This is vastly over simplified but my clients tell me all the time that I need to shut up and pretend I'm explaining things to my 5 year old niece, so there you go.