Culhwch and Olwen introduces Cilydd through his lineage and his search for a suitably noble wife. His father is Celyddon Wledig, and his chosen bride is Goleuddydd, daughter of Anlawdd Wledig. During pregnancy she becomes distressed, leaves inhabited places and wanders outside the household. She eventually gives birth where a swineherd keeps pigs, an episode that explains Culhwch's name within the story. The child is taken into care and grows up as the family's heir. This unusual birth prepares the audience for a hero whose life begins beyond the ordinary boundaries of courtly society.

After the birth, Goleuddydd falls ill and prepares for death. She asks Cilydd not to marry another woman until a particular briar grows upon her grave. Versions describe the required briar as two-headed or bearing two blossoms. The grave is kept clear for years, preventing the sign from appearing. When that care eventually lapses, Cilydd discovers that the promised condition has been fulfilled. The episode combines a husband's oath with a dead wife's attempt to delay the arrival of a stepmother, rather than establishing a historical custom or a precise royal chronology.

Cilydd's remarriage is violent. Having been told about the wife of King Doged, he attacks and kills the king, then takes his widow, her daughter and the conquered territory. The narrative does not require the audience to mistake this acquisition for an ordinary courtship. The new queen later learns that Cilydd has a son and brings Culhwch into the discussion of marriage. She proposes that he marry her daughter. Culhwch refuses, saying that he is not yet of an age to marry. His refusal concerns the daughter, not a proposal that he marry his stepmother herself.

The queen responds by declaring that Culhwch will have no wife unless he wins Olwen, daughter of the formidable giant Ysbaddaden. On hearing Olwen's name, Culhwch becomes consumed by love although he has never seen her. Cilydd advises him to seek his cousin King Arthur, ask for the customary assistance of a kinsman and request help with his suit. Arthur's recognition of the family connection makes the court available to the young man. Cilydd therefore supplies the practical advice that turns an apparently impossible condition into the beginning of an expedition.

Once Culhwch leaves, Cilydd largely drops out of the action. He does not become one of the companions who undertake Ysbaddaden's tasks or hunt Twrch Trwyth. His importance lies in the chain of events that precedes those adventures: the first marriage, the promise, the killing of Doged, the second marriage and the counsel to approach Arthur. The name Celyddon has encouraged speculation about northern British associations, but a patronymic alone does not locate a historical kingdom. Cilydd is best understood as a legendary father whose decisions connect household conflict to the wider Arthurian world.