Can I add a little bit to maybe put it in context?
Clicker training is based on something called operant conditioning, which is one of the main way all animals - including humans - learn about things.
We learn that when we do something, things happen. So when we want to cross the road, we press a little button, a green man appears and the cars stop. When we want a drink, we put some money in a machine, and a can appears
Clicker training works very like this. Horses like food - one of the first things they learn is that if they look in a funny dark place between two uprights, they find a way of suckling milk
So they're all set up to learn that there are things out there that tell them food is coming.
Say you want your horse go backwards (and to make it difficult, you want to do it without touching them
). You stand by the horse and eventually, they'll shift their weight back a little. You make a clicking sound with your tongue and then offer the horse a couple of pony nuts. Then you wait again, and the next time the horse shifts their weight backwards, you click again and offer a few pony nuts. From the horse's point of view, the world is suddenly becoming a little more predictable - "I did this, and heard that noise and food came... I might try doing the backwards thing again and see what happens..." And the backwards shifts start to happen more often, and the horse may move further backwards. You just keep clicking - to mark the exact second you saw what you wanted - and then offering the treats.
Horses learn very quickly this way - as do humans
If my boss praises me for doing something, that's nice. If my boss praises me and pays me, I'm much more likely to turn up for work tomorrow
So there's nothing magic about the click - it's just a signal that food/a scratch/something nice is coming. The magic is that the horse is suddenly very keen to work out how to get you to click, regardless of whether you're training them to back up, touch a target, do a smooth trot/walk transition or trot in shoulder-in