Who is Ciri?
Known as the "Lion Cub of Cintra," played by Freya Allan, Ciri is a princess on the run. Ciri -- whose full name, Cirilla Fiona Elen Riannon, is just as long as the kingdoms she's destined to rule -- is the princess of one of the Continent's northern kingdoms, Cintra. Her parents died before she was 5 and was subsequently raised by her complicated grandmother, Queen Calanthe (Jodhi May), who is hellbent on the slaughter of elves and other enemies and thrives on war and being in the midst of battle. She's a controversial figure, but one who clearly loves Ciri.
Ciri's introduction is violent as we meet her during the Nilfguaardian invasion of Cintra. Her grandmother and her grandmother's husband, King Eist (Björn Hlynur Haraldsson), fight in an epic, losing battle. To avoid being killed, Ciri has no choice but to flee, and her grandmother tells her that finding Geralt is her destiny. Along her journey, much like Geralt, Ciri is treated with distrust and disdain. There's a hatred reflected upon the Cintran royal family by its people because of how they chose to rule through violence.
While Ciri is only mentioned in the first two games in The Witcher series, her first real appearance comes in the third entry. She's in her early 20s in the game, while in this season of the Netflix series she's young, around 11. So Ciri's childhood, before being taken under Geralt's wing, isn't something that's been visually depicted before -- and the anticipation for Older Ciri adventures is high.
What's Ciri's connection to Geralt?
Now, this is where the show really gets confusing, especially for someone watching it who doesn't know anything about the source material. Ciri and Geralt are bound by something called the "Law of Surprise." The Law dictates that a man saved by another has to offer his savior something in return. This offering, however, is unknown to both parties so when someone says, "I invoke the Law of Surprise," you don't really know what you're going to get. In most cases, though, it takes the form of the saved party's unborn child. In saving Ciri's father, and invoking the Law, Geralt becomes her protector and thus why Ciri's grandmother, Calanthe, says that Geralt is her destiny.