The Wild Hunt is looking for Ciri in The Witcher 3; a mission to which, among others, the Strigo Geralt of Rivia and the sorceresses Yennefer and Triss stand in the way. Eredin and the other knights will try in every way to capture the young girl: but why are they in pursuit of her?
The reason why the Wild Hunt wants to find Ciri is to be found in the blood of the young daughter of the Emperor of Nilfgaard. In fact, Cirilla is the bearer of the Ancestral Blood, a special conditional inherited from her mother Pavetta. Ancestral Blood has an elven origin, being an attempt of genetic manipulation carried out by some wizards to ensure the birth of a child with extraordinary powers, who according to Ithlinne’s prophecy would one day save the elves from destruction.
But to mess up the plans was Lara Dorren, daughter of King Auberon Muircetach, who married the human Cregennan, thus removing the Ancestral Blood from a dynasty of only elves. The purpose of the Wild Hunt, in this sense, is, therefore, to recover the only known exponent who still possesses the special blood and deliver it back to the elves, thus re-establishing the plan initially prophesied: the final goal, however, is to exploit the power of Ancestral Blood to open the Portal that can travel through Space and Time, a skill long lost by elves.
Speaking of the saga starring Geralt of Rivia, here is a mod that makes The Witcher 3 playable entirely in the first person.