Stories of Chandravamsha - The Origin
It the beginning there was Vivasvan (Sun) and we are currently living is the manvantar named after his son, Vaivaswat Manu.
Vaivaswat Manu conducted a sacrifice for Mitra-Varuna under the guidance of Brahmarshi Vashishtha to get a son but his wife secretly wished for a daughter and thus they got Ila who became Sudyumna.
One day Sudyumna was out hunting and he unknowingly entered an enchanted garden. The divine garden was created by Mahadev for devi Parvati. The enchantment covering the garden would convert any man entering there into a woman.
Thus Sudyumna became Ila.
Sudyumna worshipped Mahadev and devi Parvati and asked them to be converted into a man again. Mahadev did not reverse the enchantment completely but allowed Ila/Sudyumna to switch between a man and a woman every month.
Thus for a month he was Sudyumna and then next became Ila in an endless cycle.
Once Chandra's son Budha met Ila and fell in love with her. They both were made for each other, it seems.
From Budha Ila got a son, who became famous as Pururava. Pururava, the grandson of Chandra founded the dynasty, which came to be known as Chandravamsha.
Click here to watch the story of Ila and Budha in Hindi.
Click here to watch the Ila and Budha story in English.