The story I was told while on Athos was that as Mary stood at the foot of our Lord's Cross she wept and her tears fell to the ground. Some time later a bush grew at the very spot where her tears had fallen. It was covered with many small seed pods. These pods became known as the "Tears of the Panagia".
Years later a monk was struggling in the desert, trying to learn to pray. It was very difficult for him to concentrate and focus on his prayers, and he cried before God to help him. The Mother of God appeared to him and told him to find the bush with many seed pods, take them and string them together to make a rosary and then he would be able to concentrate on his prayers. He did so and found that his prayers became much easier. Ever since then this type of "prayer rope" has been known as the "Tears of the Panagia". The beads are actually the seed pods from that type of bush, which now apparently grows wild on Athos. I bought one for my wife to use in her prayers and she loves it, finding it easier to use than the standard type of prayer rope.