Persephone was Demeter daughter and they loved each other dearly. She was also the Daughter of Zeus.
Hades came and kidnapped Demeter, having had a meeting with Zeus about how he didn't have a wife for the underworld.
Persephone denied any food offered to him by Hades and was unhappy about being kidnapped
Demeter finds out that her Daughter was kidnapped by Hades with permission from Zeus and leaves Olympus furiously withering all crops for mankind
Demeter disguises herself as an old woman and ends up in Eleusis where they help her
Zeus tells Hades to give Persephone back to Demeter but he secretly feeds her a pomegranate seed and so Persephone has to spend 1/3 of the year in the underworld with Hades.