Yeul is an enigmatic character from the beginning, she doesn't have much in-game time, as well as little dialogue. If she speaks, she does so cryptically. However, when the story unfolds it turns out she is actually a crucial character.
She is first seen being laid to rest in the sea of Valhalla by Caius Ballad, her death being seemingly Caius's motivation to fight Lightning.
It turns out later in the game, that she is a seeress priestess from the time of the war of transgression, which she foresaw five hundred years ago. Being blessed and cursed with the "Eyes of Etro" that let her see into the future, she transferred her visions to the oracle drive. However, this gift of Etro comes with a major sacrifice: every time she has a vision, her lifespan is shortened.
She dies young just to be reborn, over and over again, to continue foreseeing the future. Trapped in this cruel cycle, her fate is Caius' motivation to destroy time by killing Etro, creating a world without future where Yeul can live free from her curse.
At the end of the game Noel states that Yeul actually chooses to be reborn, so she can be with Caius.
Lightning Returns: Final Fantasy XIII
In Lightning Returns, Lightning journies to the Wildlands, the last bastion of nature in Nova Chrysalia, where she finds that Etro's temple, the last remnants of Valhalla, are now a part of it. She also learns that the temple is the origin point of the Chaos consuming the world. Inside the temple, she encounters multiple Yeuls, as well as Caius. Each and every incarnation of Yeul is now a part of the Chaos, and it is by their power that Caius cannot be freed from its grasp. The Yeuls, each a distinct lifetime with a distinct personality, keep Caius bound to the Chaos; some wish for him to receive salvation, while others want him to stay with her, but no matter what, they will not let him go and Lightning cannot use her powers to "save" him.
At the end of the game, the myriad Yeuls, as well as Caius, stay behind in the Chaos, where they will watch over the cycle of death and rebirth, taking Etro's place. However, the last of the Yeuls, the one whom Noel loves, is allowed to be free, and to be reborn in the new world where she and Noel can be together.
Her full name is Paddra Nsu-Yeul, which means "Yeul of the Nsu clan, from the city of Paddra."
She is voiced by Mariya Ise in the Japanese version, and by Amber Hood in the English version.