I think you're talking about a bridle.
Bridle
Here are some sentences.She buckled the bridle over the horse's head.The horse's bridle was green.
There really is no part of a bridle that does that, however blinders are designed to keep the horse's attention focused ahead of him. It is up to the rider to keep the horse focused. The bridle is mostly just a means to hold the bit in place which allows communication.
The section behind the horse's ear is called the bridle path. It is called the bridle path because a section a the bridle is place there and the horse will be uncomfortable if the bridle path grows out too long. There is no specific name for the process of trimming the bridle path.
the horse rider directed the bridle to turn right.
The process of putting a bridle on your horse.
A bridle or a halter controls a horse when you are walking it or the horse.
A headpiece in horse terms typically refers to the part of the bridle that goes over the horse's head and includes the crownpiece, browband, cheekpieces, and throatlatch. It is used to secure the bridle in place and provide attachment points for reins and other pieces of tack.
A bridle mount is a hook, rack or similar device that you hang bridles on when the horse is not wearing them. A horse should never be tied up in a bridle because if it panics and pulls, it can damage its mouth. It should also never be left in a bridle unnattended. Most of the time, it should wear a halter and the bridle should be hanging up. You can also hang other leather strappings, lead ropes and halters on a bridle mount.
The jockey checked that the horse's bridle was properly on.
Bridle training a horse can take a long time. You can start the horse out young however and get them used to it. While the horse is still a foal (If you have the horse while it's that young) get it used to having a leather foal halter on and lead it around gently. As the horse gets older, around a year old or so you can place a bridle (Without the bit) on it's head and begin to lead it with the bridle on. After the horse accepts this you can introduce the bit, a very gentle snaffle type bit is best, give the horse treats while it has the bit and bridle on at the same time. Again once this becomes second nature to the horse to have a bridle and bit on you can begin training the horse to follow the pressure from the bit and how to turn, move forward, and backwards. You'll need a helper for this portion of the training. Eventually the horse will accept the pressure and you will have a horse trained to the bridle.