I've read the books so I know a lot about the Wild Hunt. It's also easy to figure out what they want from Yennefer and Geralt but I don't want to ruin the fun for those who haven't read the series. So let me now divide the information for gamers who don't want book-spoiler and those who do:
Only very tiny spoilers: In the first chapter during the quest in the burned mental hospital, there are files of the patients. One of them mentions a man who claimed to have been kidnapped by the Wild Hunt and taken to "a world where genocide happened and unicorns walk on the human corpses". This is the parallel universe of the elves from the Hunt. The elves from Geralt's world are Aen Seidhe, they on the other hand are Aen Elle.
Why unicorns? In the witcher's world unicorns are sentient beings who have the power to travel between the worlds. It makes them the best ally of the elves. However, unicorns are also pacifists who despise cruelty and murder. Aen Elle murdered the whole human population in their world, leaving only a few beutiful young maidens as their slaves. The unicorns were so disgusted by this, that they turned against the elves.
The leader of the Wild Hunt is called Eredin. He isn't the real king of Aen Elle. The king and the queen are dead. Their bloodline was the only one capable of opening the gates to other worlds. Without it, Aen Elle are only able to to send their specters to other world, which is not enough for them. Eredin desires power that would enable his army to physically appear in Geralt's world.
HUGE SPOILER FROM THE BOOKS AND SPECULATION ABOUT W3 PLOT
LikeIsaidEredinwantsthepowertoopenthegatestofotheruniversesandthebloodlineallowingitgotlost.There'sonlyonepers onofthatbloodlineleftalive-GeraltandYennefer'sadopteddaughter,Ciri.AttheendoftheseriesCiriescapesEredinandhesw earstofindheronedaysoit'smytheorythatEredinnowwantsttouseGeraltnadYennefertolureCiritohim.
END OF THE SPOILERY-SPECULATION.