In the beginning of the book and the HBO series entitled Game of Thrones, Jon Snow’s mother was unknown. He was said to be the bastard son of Eddard “Ned” Stark, a claim which angered Catelyn “Cat” Stark. However, fans of the book already speculated that Jon Snow was a Targaryen because of Lyanna’s last words: “Promise me, Ned.”
It was revealed in the finale episode of the seventh season of Game of Thrones that Jon Snow is in fact Aegon Targaryen and he was the son of Rhaegar Targaryen and Lyanna Stark. Nobody knows what will become of Jon Snow since the books are not yet done and the final season of Game of Thrones is not yet released.