Rein chains are simple connectors between a bridle bit and romal reins, they vary in styles, links, swivels, balls, etc.. They send soft signals and vibrations to the horse that can't be achieved with the reins connected directly to the bit. They also protect your romals from getting wet when a horse drinks. They refine signals from the riders hands to the horse. You can see them on this picture of one of my bridle horses.
~Started young horses in Bosca te Ador, unto the two rein the old Spanish spade, brought them along with two hands that were gentle. Some fine reining horses as ever were made~