Goleuddydd was born into the house of Anlawdd Wledig, a figure whose name appears in Welsh genealogies and pedigrees as a king of Britain, though his historical existence is as shadowy as that of Arthur himself. Anlawdd's other daughter was Eigr, called Igraine in the later French and English romances, the woman who married Uther Pendragon and became the mother of Arthur. Goleuddydd's sisterhood with Eigr made her Arthur's aunt, and it was this kinship that would prove decisive when her son Culhwch, grown to manhood, rode to Arthur's court at Celliwig in Cornwall and claimed the king's aid as his first cousin. The genealogies that bind Goleuddydd to Arthur are not merely decorative. In the oldest Arthurian tale, kinship is power, and the blood that flows from Anlawdd Wledig connects the greatest king in Britain to the boy who would hunt the enchanted boar Twrch Trwyth and win the daughter of a giant.

Cilydd son of Celyddon Wledig desired a wife as well born as himself, and the woman he chose was Goleuddydd. The tale records that after their wedding night, the country went to prayer so that they might have offspring, and through the prayers of the people they obtained a son. But from the hour she became pregnant, Goleuddydd went mad. She did not come near to habitation. She wandered the countryside, living outdoors, sleeping in the wild, her mind unmoored from the court and the comforts of her husband's hall. The text does not say what caused the madness, whether it was the pregnancy itself, a curse, or the touch of some supernatural force, but the image is haunting: a queen of Britain, daughter of a wledig, wandering like a wild thing through the forests and fields while the child grew within her.

When her time of delivery came upon her, her senses returned. She came to her proper reason, as the text says, at a place where a swineherd was tending a herd of pigs. The pigs frightened her, and in her fear she gave birth. The swineherd found the child, took him from the pig-run, and brought him to the court to be baptised. The boy was named Culhwch, from the Welsh cul meaning narrow or slim and hwch meaning sow or pig, a name that the redactor of the tale understood to mean pig-run, though the scholar Idris Foster pointed out that cul in the sense of sty is not known from so early a period, suggesting that the name may originally have meant something else, perhaps slim pig, and that the pig-run story may be a folk etymology invented to explain a name whose true meaning had been lost. Whatever the origin, the name bound the boy to the place of his birth, and Goleuddydd, having delivered him in the mud and fear of a swine-run, was left weakened and dying.

The illness that followed the birth was mortal. Goleuddydd knew she would not survive, and she turned her mind to protecting her son from the fate that awaited the children of widowed kings. She called her husband to her bedside and made him promise: he would not take another wife until he saw a briar with two heads, two blossoms, growing upon her grave. Cilydd swore the oath, and Goleuddydd, not content with a mere promise, summoned her confessor and commanded him to visit her grave every year and strip it bare, trimming it so that nothing might grow upon it. She knew that as long as the grave remained bare, her husband would remain bound to her memory, and her son would remain safe from a stepmother's ambition. The confessor agreed, and Goleuddydd died.

For seven years the plan held. Cilydd sent a lad every morning to look upon the grave, and every morning the lad returned with the same report: nothing grew there. The confessor kept his word, or seemed to, trimming the earth so that no blade of grass, no briar, no weed could take root. But at the end of seven years, the confessor failed. Whether he grew lazy, or forgetful, or whether some other hand stayed his, the text does not say. What it says is that one day, while Cilydd was out hunting, he made for the graveyard, for he wished to see the grave whereby he would get a wife. And there, growing upon the bare earth where nothing should have been, was a briar with two blossoms upon it. The oath was broken, and Cilydd was free to marry again.

The new wife was the widow of King Doged, a man whom Cilydd killed in order to take his wife, his daughter, and his land. The marriage was swift and brutal, and the new queen brought with her a daughter of her own. When she learned that Culhwch existed, that he was the heir to Cilydd's kingdom and that her own daughter would inherit nothing while he lived, she conceived a plan. She suggested that Culhwch marry her daughter, a union that would unite the two lines and secure the succession. Culhwch refused. The queen, enraged, cursed him. She swore a destiny upon him: he would marry no one but Olwen, the daughter of Ysbaddaden Pencawr, the chief of giants, a woman so dangerous to seek that no man who had ever looked for her had been seen again. The curse was binding, and Culhwch, though he had never seen Olwen, fell under its power. He set out for Arthur's court, claimed his kinship, and began the quest that would occupy the longest and earliest of all Arthurian tales.

Goleuddydd never appears again in the narrative after her death. Unlike other mothers in Welsh mythology, such as Rhiannon in the First Branch of the Mabinogi, who suffers penance and is eventually restored, or Penarddun in the Second Branch, whose children shape the destiny of Britain, Goleuddydd is gone from the story the moment her grave is bare. Yet her absence is the engine of everything that follows. Without her death, there is no stepmother. Without the stepmother, there is no curse. Without the curse, there is no quest for Olwen, no hunt for Twrch Trwyth, no catalogue of Arthur's warriors, and no demonstration of the king's power to obtain the impossible. The scholar Stephen Knight, in his analysis of the tale, identified the central fear of Culhwch and Olwen as the failure of a family to reproduce itself, the threat of a sterile generation and of reproductive power lying in enemy hands. Goleuddydd's death embodies that fear. Her grave, kept bare by a confessor's hand, is the symbol of a kingdom without a queen, and the briar that finally grows upon it is the symbol of a fertility that can no longer be denied, even at the cost of the heir's safety.