Story of Urvashi and King Pururavas is found in the Srimad Bhagavad Purana and Padma Purana. Pururavas was the son of Budha and Ila. He was a great ruler and warrior. He even won several battles for Indra by defeating demons that tormented heaven and earth.
While Pururavas was ruling earth, Urvashi the celestial maiden was cursed by Brahma to be born on earth (In some Puranas it is mentioned that she was cursed by Sage Bharata).
Urvashi who had heard about the greatness of Pururavas met him. The king was bewitched by the beauty of Apsara Urvashi and wanted to marry her.
She agreed to marry him on three conditions:
He would keep her two lambs under safe protection.
He would allow her to live on ghee.
He would never appear naked before her.
The king agreed to all the conditions and lived happily with her.
Urvashi was one of the greatest dancers in heaven and Indra and other Devas were missing her. So they decided to get her back to heaven.
Gandharvas were deputed to bring back Urvashi.
One dark night rainy night when there was lightning the Gandharvas stole the lambs of Urvashi. The lambs let out a cry. Urvashi cried for help and the king jumped out of bed. Suddenly there was a lightning and Urvashi saw the naked form of the king. Two conditions were broken and Urvashi returned to heaven.
Pururavas was in great dejection. He roamed around in search of Urvashi and after several years discovered her in Kurukshetra. Urvashi immediately recognized the king and she came to him. She bore him several sons and the couple lived happily for several years.
Note – There are numerous subplots in the story like Pururavas was cursed by Acharya Tumburu of heaven that he will be separated from Urvashi.