A sole is used in the Spirits of the Elid quest. Players make two of them by taking the shoes from the mayor of Nardah's house, and right clicking them and selecting "remove-soles", or simply clicking on them in your inventory.
Towards the end of the quest, the player must give these to the genie who lives in the crevice to the west of Nardah in exchange for the Statuette of Elidinis.
As only one sole is needed, the second can be dropped as it is rendered useless. It can also be used to acquire a duplicate of the statuette using the drop trick - the statuette has no use after the quest however.