Persephone is goddess of springtime and her mother is Demeter and her dad is Zeus. On a summer day she was picking flowers with some nymphs. Hades took an interest in her and made her his wife. Demeter was heartbroken when she found out. However Persephone was allowed to go to the world above with Demeter for half the year and the rest of it with Hades.
After the film, the crew was not quite sure that she could be in the series, though there was a plan that she could be in the episode "Hercules and the Underworld Takeover". However Hecate was going to takeover the Underworld and become queen which is exactly what Persephone is.
Contrary to seemingly popular opinion, she never actually appeared in the show. According to an inside source from the show, several different stories were considered for her, including one where she was the daughter of Hades and Demeter who were embroiled in a custody battle, and another where she would have been a teacher at Prometheus Academy, but nothing ever felt really appropriate and her storyline was dropped.