Okay, so Kate could give you a much better explanation, but the Spanish Walk is basically a dressage thing, where the horse throws out his front legs as high and as far as he can. Beautiful! Here's a pic with a pretty good example:
And on side note- that horse is gorgeous!!!
And here's a video I found on youtube. Looks like it's made by a fellow Parelli person! :D I think this is the one that Kate is basing her method off of.
And for some strange reason, the program isn't letting me copy as a link.....grrr...I hate computers. x)