The Counter Bend... a LOT of people do it on accident, but some people do it on purpose and it can be a fantastic training exercise. When done on accident, it looks very crude. Usually it happens to the unsuspecting rider who is trying to steer their horse by neck reining, but they cross the outside rein over the midline and unknowingly pull the horse's nose the opposite the direction of travel. This ends up making the horse dump his weight on the inside shoulder (if turning left, it dumps weight on left forequarter, and vice versa) and so the horse bottle spins (swings its rear to the outside of the turn) because the weight is on the forehand, and that just kills the athleticism and efficiency of the horse, and in the end it is simply a very ugly sight.
Where as, when the counter bend is executed correctly, the rein position is the same (as shown in the image below), meaning the outside rein is over midline, BUT the weight is put on the inside hind of the turn, in this case the left hind, though the bend is to the outside of the turn, in this case to the right (also shown in the image below).
I love the mental and physical gymnastic benefits of teaching the horse this move. Mentally it requires the horse to tune in and focus on our body position and trajectory. They cannot see the direction of travel very well, so for me it shows trust as much as anything, and if they follow you with trust, it is performed even better; smoother, more rhythmic, more effort. Physically it is like us doing kinesthetic exercises which is "learning through feeling, such as a sense of body position..." They learn how to follow our lead or direction, through their range(s) of motion.
This exercise is one of those exercises I hold off on teaching a student because though it is powerful for the horse, it can be super confusing to the human. It's one of those rub-your-belly-and-pat-your-head kind of things, and maybe even do it while chewing bubble gum just for the challenge of it ;-) Notice in the image I'm using below, where my weight is and where my hand is. I am executing a left counter bend, so the horse is arced right (in this case he is cantering, so he's also counter cantering) on the right lead, but we are traveling left. My head and shoulders are back over his left hind, the same as if I were asking him to do a normal left turn or arc around to the left. Also notice I'm looking right, the same way he's looking, this is super important in the beginning because it keeps your body position "correct" for the counter (opposite) bend, which is in this case a right lead position on my part i.e. left leg back a little, right leg forward a little. By keeping my weight back over his left hind, I am encouraging him to put his weight there as well, lightening his front end, most especially the right forequarter or shoulder.
The magic is that it is a mental game of twister for the horse, and the results are that you end up developing a nice light and straight inside shoulder. And that is one of the nemesis of teaching the horse to be efficient and athletic because it is so much easier for the horse to lean and dump his weight on that inside forequarter, instead of the lifting and pushing with the inside hindquarter.
To keep it simple, #1 always think about riding your horse's hind legs, meaning keep your head and shoulders back over an inside hind leg (inside = left hind if you are turning left, right hind if you are turning right). And #2, look the direction your horse is looking...this is imperative when you are first learning. I can look all around and talk to people etc, but keep my body correct so as not to confuse the horse, because I'm used to doing this move and can isolate my lower body from my upper body. But when you are learning it is best to simply put your nose where you are putting your horse's nose. Once you and your horse get good at it, it is a lot of fun to do and very useful, if not critical, for the horse to have in his vocabulary of principle maneuvers.