Ciri is daughter of emperor Emhir(she doesn't know that) and Paveta, daughter of Calante, queen of Cintra. Ciri is the result of a failed genetic experiment carefully conducted by mages for a long time, that went awry when Lara Dorren aep Shiadhal(an elf) falled in love with a human- Cregennan of Lod, after which the mages lost trace of the genes of the Elder Blood(it grants the power to travel time and space- (without a TARDIS, that is)). Emperor Emhir was cursed to look like a hedgehog(he was going by the name of Duny then, and was not yet emperor) and Geralt lifted the curse and as a reward the emperor promised
"What you find at home yet don't expect"- i.e. princess Cirila of Cintra. When Ciri was young her parents died in a shipwreck. She was supposed to be on the ship, but her grandmother actually prevented that. The shipwreck was organised by a powerful sorcerer- Vilgefortz and was aimed at "killing" Duny so he can become emperor of Nilfgard, however durin the wreck his wife Paveta accidentally died.
Later when emperor Emhir invaded Cintra in search of Ciri her grandmother- Calante died, but Ciri managed to escape and Geralt found her, adopted her and trained her in Kaer Morhen in witcher combat styles(without the mutation), but the witchers discovered that Ciri had magic powers and that she is in fact a Source, so Geralt send her to Yennefer, that trained her in magic. Yennefer, Ciri and Geralt visited the Thaned island for a mage conference, but pro- Nilfgaard mages organised a coup and fighting ensued. Ciri fleed Vilgefortz to a tower with a teleport and accidentally teleported to a desert. From then on Geralt and Yennefer actively searched for her, while she was in Nilfgaard, where she briefly joined a bandit group called the Rats(and had hot kinky sex with another girl), but since the Rats were bandits a local baron hired a legendary mercenary(no, not Big Boss)- Leo Bonhart(a remarkable swordsman, that had even killed witchers and defeated the Rats single- handedly) that killed them and captured Ciri, forcing her to fight in a gladiator fight, after deducing she had been trained by witchers.
By that time everyone was looking for Ciri- she was an immense source of magic and everybody wanted to impregnate her, because it is said that her children would be even more powerful: the emperor of Nilfgaard- not as a father, but to mary her and have her children, Vilgefortz, again for her children,the Lodge of sorceresses, which wanted to mary her to the prince of Kovir, and yes have her children, the Wild hunt(elves from a parallel universe where they are the dominant race and humans are slaves)- what a surprise, again for her children and Geralt and Yenefer were the only ones that wanted to rescue her.
Eventually Ciri and Yennefer are captured by Vilgefortz and Geralt assaults his castle with his friends, which all die,- Kahir(a Nilfgardian soldier, tasked to bring Ciri to the emperor, but falls in love with her and switches allegiance), Milva(an archer, living with the dryads that helped Geralt recover after he was injured in the Thaned coup), Regis(a centuries- old vampire that eventually befriends Geralt) and Angoulême(a bandit girl Geralt rescued from hanging). Geralt and Yennefer kill Vilgefortz and Ciri kills Bonhart(in an awesome fight on wooden beams).
As Geralt, Yennefer and Ciri exit Vilgefortz's castle, wary and injured from battle, they are met by the emperor oof Nilfgaard that takes away Ciri, promising to her adoptive parents to never make her cry. Geralt deduces that the man before him is infact Duny the hedgehog, whom he saved from a curse years ago, and since only Geralt and Yennefer know Emhir's true identity they are offered to take a hot bath(and have sex for the last time) and commit suicide. But when they call for the guards to give them knives Ciri appears and tells them that the emperor and his troops had left. Ciri, part of her hair had now turned white, again loosing Geralt and Yennefer after just finding them and after the horrors that Bonhart, Vilgefotz and the Wild hunt(she was briefly caputered, but escaped with the help of unicorns) took her through finally broke her and she cried- emperor Emhir, seeing he had broken his promise to Geralt and Yennefer leaves without Ciri.
On the return journey Geralt is in Rivia when a massacre of non- humans ensues. He spares a peasant with a pitchfork, but the peasant stabs him in the stomach. Yennefer arrives and literally drains her powers and live trying to save Geralt. Then Ciri arrives and seeing Geralt and Yennefer dead sort of heals them and takes them away to the isle of Avalach, after which she teleports to another world(that seems to be the one from the legend of king Arthur).
Here ends the last book and the first game is set five years later during which we know not what happened to Ciri, but the presumption is that the Wild Hunt is still actively chasing her through the worlds and times and she has finally returned to the world of the Witcher.
PS. Sorry if I misspelled, but english is not my native language and I have not read the saga in english. Even after 10+ years of studying the language I am bewildered by the names, in my language you read what you write, in english you write Jo
hn, but read it Jon or even worse- you write queue, but God knows why you read it ku:
PS2. God helps anyone that tries to compare The Witcher with Game of Thrones/ A Song of Ice and Fire: the first witcher short story was published in 1986, the first book of the saga in 1994, while the book A Game of Thrones was published in 1996.
I recommend reading the saga too, but it is not needed as much. There are also very good summarys of the book on the internet.