At this moment in the show, Nilfgaardian forces are on the verge of taking over the Continent, and they seem to have a considerable advantage after the Thanedd Coup. The Battle of Sodden Hill was a blow for Emhyr and Nilfgaard, as it proved that no emperors could enforce their tyranny as long as the Mages were there to keep them in check. Emhyr bounces back by destroying the Brotherhood from within — the coup at Thanedd allowed Emhyr to employ his Scoia’tael ambush with greater precision, and singlehandedly dismantle one of the most crucial power structures in the Continent. As Vilgefortz (Mahesh Jadu) was Emhyr’s spy all along, the Brotherhood was compromised from the get-go, and Tissaia’s (MyAnna Buring) death only intensifies the precarious position in which the Mages currently find themselves.
The show adapts the Imposter Ciri storyline directly from the books, where a fake Ciri is implanted by Vilgefortz to distract Emhyr from the real one, as Vilgefortz intends to use her Elder Blood for his own ends. At the end of season 3, we see fake Ciri arriving at Nilfgaard and Emhyr accepting her by his side. In the books, Emhyr is aware of Vilgefortz’s trickery but still accepts fake Ciri in order to strengthen his dominion over the Northern Kingdoms. However, as the world at large does not know that Emhyr is Duny (Ciri’s biological father), how does Emhyr plan to use Ciri to strengthen his claim over the throne? This is where things get icky in the books: He marries her and plans to impregnate her to help fulfill Ithlinne’s prophecy.
In essence, marrying the Lion Cub of Cintra automatically legitimizes Emhyr’s rule beyond his coercive tactics, and Ciri’s child serves the purpose of thwarting the White Frost.