Stallions are adult male ponies. Younger male ponies are called colts.
The anatomy of a male pony in the animation style of Friendship is Magic differs from that of a female pony in several small ways. The most noticeable difference is the shape of the skull; whereas a mare's muzzle is more rounded, a stallion's is distinctly more square. Stallions also tend to be slightly larger than female ponies, and have straighter backs and less curved body parts.
In the Show
Given the intended demographic of the show, the majority of the main and secondary cast tend to be female, all the way from the mane six, to Celestia, to the Cutie Mark Crusaders, to Zecora. Very few supporting characters are male, some of them being characters like Snips and Snails, Fancypants, Big MacIntosh, Mr. Cake, and Soarin.