Daphne was a very beautiful nymph, who was the daughter of the river god, Peneus.
After Apollo made fun of Cupid for being too young to weild a weapon, Cupid shot him and Daphne with his arrows of love as revenge.
Daphne, afraid of marriage went to her father, Peneus. She begged for him to never let her be wed, for she wanted to be like the Goddess Artemis. He granted her the wish, but warned her that her beauty will get her into trouble anyways.
Apollo, after being shot by Cupid, went on a journey to find Daphne to ask for her hand in marriage.
Apollo finally found Daphne, and attempted to swoon her into marriage. Daphne did not want this to happen.
And so, Daphne's father turned her into a laurel tree in order to protect her from being chased by the God Apollo.