Horses are highly intelligent, and they can be taught all sorts of different behaviors beyond those used in riding. The girl in this video is training her horse to identify a picture of a horse when presented with pictures of different animal types. The training looks to be quite effective so far, with the horse correctly identifying the horse picture repeatedly.
This young trainer is using clicker training to teach her horse the desired behavior. According to Equine Clicker Training, clicker training is a highly useful tool, especially for horses. Clicker training relies on positive reinforcement to praise your horse when he performs a desired behavior. In the case of clicker training, the praise your horse receives is the sound of a clicker - a device that you hold and click, or even just the sound of you clucking your tongue.
During initial clicker training, you pair the sound of the clicker with a reward - food-based rewards are pretty effective. As your horse learns that the clicker is a positive sound, you can gradually decrease and then eliminate the food reward altogether.
Clicker training is very flexible and can be used to reinforce virtually any behavior. By isolating smaller behaviors, like lifting a leg or turning a head, you can create the building blocks you need to teach your horse larger tricks or behaviors, like stepping up onto a stool or even lying down.
The key to clicker training is repetition, as your horse needs to understand what behavior you are rewarding. Once he understands that a behavior is desired, your training can progress as you further tailor or develop that behavior into a larger trick.
Clicker training has a largely positive reputation in the horse world since there is no discipline involved. Horses which have been clicker trained are often willing to perform desired behaviors, having come to know that they will receive praise and reward when they do a certain behavior.
Want to get started with clicker training? There are many resources available online, but many horse trainers should also be able to help you get started.