Slow feeding is to, by use of some mechanical device (usually a restricting feeder); make it impossible for the horse to fill his mouth with hay. By slowing down the eating pace the same amount of hay will last longer and therefore will keep the horse occupied and stimulated for a longer period of time. It basically replicates grazing but in a controlled manner. It also allows you to control the sugar levels in your horses' diet and the quantity fed by eliminating insulin spikes.
A free roaming horse spends most of his waking hours searching for food. Since horses only sleep about 4 hours per day and seldom for longer periods than about 20 minutes, food is their main focus for about 18-20 hours a day. Many traditionally kept horses are still being fed 2-3 (or maybe 4) times per day and often more than they will eat in an hour or two each time.
Slow feeding your horse allows them to eat for longer periods of time, without feeding them more.
To really understand how horrific these traditional feeding methods are to the horse we need more knowledge about how a horse's digestive system works than most people have.
The horse's receptors for feeling content and full is located in his chewing muscles and not his stomach. This makes it essential that he chews his food slowly and rigorously. If he eats too fast he will not feel content, therefore overeat if he has the chance, or else feel stressed over the fact that he never becomes content. He will think he is starving to death even though he is not, and that might very well make him nervous and edgy. By restricting his possibilities to rush through his daily ration, he will chew every single strand much more rigorously, therefore preparing the food much better for digestion and reaching the chewing level where he feels content and happy with the amount of food her receives.