The horse uses his head and neck somewhat separately from his body to help maintain his balance, almost as a counterweight. When you ask the horse to bend, such as when you go around a corner, you use your hips, shoulders, inside leg and a slight inside rein. The outside rein and leg are equally important, as they keep the horse aligned nose-to-tail. Many riders minimize the impact of these outer aids, mainly because the way a rider's mind works goes against the way a horse's body works.
From where the rider is sitting, her eyes are directed to the horse's head and she may be tempted to apply the reins like a steering wheel. The problem is that the only part of the horse she's really steering is the head, which can go one way while his body goes the other way. Eventually the body will get there as well but not in a very balanced manner - picture a green 6-year-old child trying to steer a pony.
To better control the horse's body, the rider should rely more on her posture, seat and legs than her hands, and to do that the outside rein has to stay in contact with the horse's neck. Remember: The outside rein controls and steadies the horse.
When you're riding in a ring and you approach a corner, the horse becomes heavier on his inside shoulder unless he's been conditioned to carry more weight to his hindquarters, like upper-level dressage horses, open jumpers and reiners. The tendency to become heavier on the inside shoulder is accentuated when the weight of the rider is added to the horse's task.
As the horse and rider go around the ring, they tend to fall into the corners and drift in from the rail. In an effort to keep the horse from drifting in too much, the rider may want to open her outside hand. But, since the horse's body tends to move away from the head, that hand coming off the neck keeps only the horse's head near the rail. The rest of the horse's body swings even more to the inside.
Basically, if you want to keep your horse's head and neck in line with the rest of his body - and for you to be able to point the entire horse where you want him to go - the outside rein should never come off the neck.
The correct position actually begins with the inside rein, which should widen slightly away from the withers, just enough to direct the horse's nose to the inside. The rider should be able to see just the horse's eyelash in front of the cheek piece of the bridle. Any more neck bend than that and the horse will become rigid through his top line or possibly escape sideways through his outside shoulder. This slight inside neck bend will create a bulge in the outside of the neck where the rider can place her outside rein. Overall, you are looking for bend under the rider's inside leg, not so much through the neck.
The rider will now be able to use her outside rein to keep the shoulders in line with the hindquarters, an action also known as "shoulder-fore." When the horse is straight nose-to-tail, it's much easier for the rider to use the inside leg to keep the horse in the track on the long side of the arena and to stay balanced through the corners.
Another important element in keeping the horse's body straight on the line of travel is that the rider's shoulders should be parallel to the horse's shoulders while her hips are parallel to the horse's hips. Her shoulders should go in the same direction that she wants her horse's shoulders to go. Many people lead with their inside shoulder on corners and circles, and this has the effect of turning the horse's shoulders to the outside, thus bringing the rider's outside hand off the neck.
While it may seem counterintuitive at first, the rider should practice turning at the waist when starting any corner or circle so that her upper body faces through the turn. The inside hip goes forward and the inside shoulder goes back so they are aligned with each other. Most of the time, you can make the horse turn by not doing anything with your hands at all, just by turning at the waist so that your inside shoulder comes back.
This places the outside rein more in contact with the outside neck/shoulder and brings the forehand around the haunches. That one simple motion of the rider's waist and shoulders allows the horse's whole body to turn.