This is a zebra. (Image source: Joachim Huber via Wikimedia Commons). As you can see, she has no withers.
This is a Quarter Horse. Withers.
Equines that have never been domesticated do not have much in the way of withers. The zebra has the very beginnings of them, but it's nothing compared to that of the Quarter Horse.
So, why is this?
There are two possible answers, which have worked together to create the withers.
The spines of the withers provide an elevated and stable anchor point for certain muscles in the shoulder. The higher withers of the domestic horse (and this can be seen in the unusually high "shark fin" withers of racing horses) raise the shoulder muscles, increasing the reach of the forelegs, which increases stride length and thus short distance speed. This is not an advantage over longer distances and may even be a slight disadvantage, explaining why wild horses, that rarely sprint, have never evolved high withers.
The other reason is deliberate selection for higher withers (within reason - those shark fins are actually a pain). A moderate wither height anchors the front of the saddle, except on gaited horses, helping prevent it from slipping sideways. Little or no wither is considered a fault, especially in riding horses - in the US this is called "mutton withers." With horses that have no wither, and this is more common in ponies, extra straps are often needed to ensure the saddle stays in place. Donkeys tend to have lower withers, in no small part because donkeys are seldom used for speed work and are more commonly used for harness work than for riding, so there's less selection pressure.