It's an English term. English reins have a buckle in the center. Riding on the buckle means that you are riding with such loose reins that you are actually holding the buckle. It indicates that your horse is so lay back that you don't need contact with his mouth at all times. (Pays to have once been an English rider )
Thanks, iridehorses that makes sense now. I am an english rider and had never heard the term before, but kept reading it in the ads for these eventing horses I am looking at.