The Spanish Walk is a movement about which many people consider to be a trick, used only in performances (mostly by Baroque horses, such as Andalusians). It is a slow, elevated walk where the movement of the front legs very high and extended well out in front of the body.
Very few “dressage” riders train the movement because, while it does show a degree of collection, it is a movement that can be very disuniting for the horse (the front legs can end up working quite differently than the hind end). But there are some benefits to it as well. It can help enhance freedom through the shoulders and, when trained properly, can help teach collection.
Its roots are classical. The Spanish Walk was trained as far back as the Romans and it’s been part of the Haute Ecole for centuries.
Here’s an example of a horse that has excellent technique. Note that in this case the horse continues to, well, walk. In many of the exhibitions where this movement is performed the walk is sacrificed and the horse merely picks its front legs up high.