Hand of the Prophets is a religious title, much alike "Emissary of the Prophets" and "Avatar of Peace", in Bajoran religion. The Hand is destined to be the Prophets main agent in linear time and help prepare Bajor for the coming threat of the Ascendants, and to unite different factions against them. The Hand is also supposed to know everything about the Ascendants by learning from their victims and teach others of the dangers they pose. The Hand also carries out tasks on behalf of the Emissary.
It was revealed in a vision from the Prophets that Captain Kira Nerys was the Hand of the Prophets, she accepted this role and learned much about the Ascendants by looking into the minds of the Eav'oq, a race driven into collective hiding by the Ascendants. (DS9 novel: Warpath)