What is the meaning of the Rukn al-Yamani, what is its relation to the Black Stone, and does it have a story?

The Kaaba has four corners: the Black Stone Corner, the Northern Corner, the Western Corner, and the Yemeni Corner. The circumambulator touches the Yemeni Corner but does not kiss it, nor does he point to it if unable to touch it, nor does he say 'Allahu Akbar' when touching it. Between it and the Black Stone, he says: "Our Lord, grant us good in this world and good in the Hereafter, and protect us from the torment of the Fire."

It is legislated to touch and kiss the Black Stone. If that is difficult, one may touch it with his hand and then kiss his hand. Otherwise, he should point to it without kissing. It is not legislated to touch the Northern or Western Corners.