The 'floating lights' that appear on Rapunzel's birthday are actually floating lanterns released by the king and queen in remembrance of their lost daughter. Unbeknownst to Rapunzel, she is that lost princess. The lights represent her parents' enduring hope and love for her, and they are a significant symbol of her true identity and destiny. This beautiful spectacle sparks Rapunzel's curiosity and fuels her dream to leave the tower and see the lights in person, setting the stage for her grand adventure in 'Tangled'.