Her father is fated to die if she ever marries, so when Culhwch (sometimes spelled as Kilhwch) comes to court her, he is given a series of immensely difficult tasks which he must complete before he can win her hand. With the help of his cousin King Arthur, Culhwch succeeds and the giant dies, allowing Olwen to marry her suitor.
The name "Olwen" reappears in the folktaleEinion and Olwen, about a sheep herder who travels to the Otherworld to marry Olwen. The tale was collected at the turn of the 20th century but is certainly related to Culhwch and Olwen.
The meaning of the name Olwen is "white footprint".  According to legend, she was so gentle and fragile that white lilies would grow in her footprints.