A peacock stirrup is a stirrup that is open on the outside. The gap is filled with either a rubber band or a leather loop.
Peacock stirrups are most often seen when an English trained horse is being ridden by a child. Some lesson barns also use them. The point is that if the rider falls, the loop will quickly release their foot from the stirrup, preventing dragging. Experienced riders almost never use them. (Also, if the band comes off it could land anywhere and then apparently they're impossible to find).