Wow..........there are entire books written on this subject. A little knowledge can be a very dangerous thing, but briefly-
What is it -
It's when you have two lunge lines (long reins......) attached to either a lunge cavesson or the bit. The person stands behind the horse & walks along behind it.
Why do it -
Its a very good way of getting the horse to go forward independently without a lead. It's far closer to riding than lunging is, & is a very good way of accustomising young horses to the sights & sounds associated with roadwork. The horse begins to learn basic diagonal aids.
How do you it -
With great skill!!
It's an aquired art, & you really need to learn from someone who has some experience.
The lunge lines need to be attached to either side of the lunge cavesson (yes thats why they have so many rings on the noseband!!) or if you are very experienced & have good hands, to the bit. The reins should be secured either by running them through the rings on a breaking roller, or through the run down stirrups (which should be as short as possible) on a saddle. If you are using the stirrups on the saddle you will need to secure them by tieing them together underneath the horses stomach. It is far preferable to use a breaking roller as the rings are in the correct place to duplicate the action of the riders hands, whereas using a saddle with the reins through the stirrups can generate a more downward action on the horses head / mouth.
The person stands behind the horse at a suitable distance - not too near but not too far either, & encourages the horse to move forwards vocally, & may then very quietly & gradually move the reins against the horses sides as well - thus the horse can begin to associate pressure on his sides with being required to go forwards. Hand aids are the same but must be employed sympathetically especially if reining from the bit.
It goes without saying that early lessons must be carried out in an enclosed area, & even when the horse is responding well enough to the aids to be taken out on the roads you really must have a second person with you.
Totally agree with all the above, and have used it for years bringing horses on. However, I do wonder why long reining is considered such an art form while lungeing can apparently be done by any fool with a cavesson and lunge line? To be perfectly honest, I would prefer a horse to be long reined (in cavesson rather than direct to the bit if the handler isn't experienced) any day over lungeing. Continual circling at any pace just isn't good for legs or backs. Long reining replicates riding more closely, and once the horse and rider are experienced it can offer a lot more variety than lungeing. There is a bit of a knack and a certain amount of co-ordination and independent hands needed - but there is with riding too. Kelly Marks' books are pretty handy if you need to learn more.
I've always used long reining more than lunging when breaking in, & agree that both are highly skilled jobs that shouldn't be taken on without the necessary experience & training. Having said that I would also say though that a relatively inexperienced person armed with a good book, a patient horse, & a lot of common sense could quite easily become competent at both. Neither skills are particularly complex, but both require a huge amount of 'feel' & some understanding of the way a horses mind works.