Snow's granddaughter is one of the few known members of President Snow's family, and perhaps one of the only people he truly held affection for.
In the books, she is only mentioned in passing at the end of Mockingjay; Johanna Mason mentions her possible participation in a proposed 76th Hunger Games involving the children of the Capitol. Although it is not her fault, some of the other victors believe the same about the tributes from the districts. They also want her to participate as she is one of the most, if not the most, important of the Capitol children. Johanna Mason and Enobaria vote for a final Hunger Games as vengeance, whereas Beetee Latier, Annie Cresta and Peeta Mellark vote against, citing that the Games were what they fought against to begin with and they need reconciliation. Katniss Everdeen votes for the Games in an attempt to make President Coin lower her guard (in movie) and for Prim's death (in book), and Haymitch Abernathy votes likewise to support Katniss. Coin tells Snow before his intended execution that they intend to hold the final Games with his granddaughter.
However, the plan for the final Hunger Games is forgotten after President Coin is killed by Katniss moments later; it was never known to anyone except Coin (who proposed it), Snow and the surviving victors, and Snow himself dies moments after Coin. Snow's granddaughter and her family are presumably shown mercy.
She is also seen in the film adaptation of Catching Fire, and appears to look up to Katniss Everdeen as an image and role model. She makes her first appearance in Catching Fire wearing her hair in a braid like Katniss wore in the 74th Hunger Games. When President Snow questions when she started wearing it like that, she replies "This is how every one at school is wearing it, Grandpa," as it is a trend in the Capitol. Unsurprisingly, Snow barely hides his displeasure. However, he does genuinely seem to care about her: When she is watching Katniss tearfully hug Peeta in the Hunger Games after Finnick Odair revives him, she says "Someday, I want to love someone that much." Snow beams at her and says, "And so you shall, my darling. So you shall."
In Mockingjay: Part 1, Snow declares association with the Mockingjay illegal and an act of treason, including symbols associated with her, and that traitors shall pay the ultimate price. His granddaughter quickly realizes what the braid represents and undoes it during Snow's announcement.