headstall
The part of a horse’s bridle that fits around its head.
A headstall is the part of a horse's bridle that fits around the animal's head, holding the bit in place. Think of it as the framework that keeps everything secure: leather or synthetic straps go over the horse's poll (the top of its head behind the ears), down the sides of its face, and under its throat. Without the headstall, the metal bit that rests in the horse's mouth would simply fall out.
When you watch someone saddle up a horse, the headstall is what they carefully slip over the horse's ears and adjust so it sits comfortably but firmly. The reins attach to the bit, and the bit attaches to the headstall, creating the connection that lets a rider communicate with their horse through gentle pressure.
Some people call the entire bridle a headstall, though technically it's just the head-fitting portion. Western riders and English riders both use headstalls, though they may look slightly different in style and decoration.