From Wiki:
The myth of Persephone, the chtonic goddess of the Underworld, also prominently features the pomegranate. In one version of Greek mythology, Persephone was kidnapped by Hades and taken off to live in the underworld as his wife. Her mother, Demeter (goddess of the Harvest), went into mourning for her lost daughter and thus all green things ceased to grow. Zeus, the highest ranking of the Greek gods, could not leave the Earth to die, so he commanded Hades to return Persephone. It was the rule of the Fates that anyone who consumed food or drink in the Underworld was doomed to spend eternity there. Persephone had no food, but Hades tricked her into eating four pomegranate seeds while she was still his prisoner and so, because of this, she was condemned to spend four months in the Underworld every year. During these four months, when Persephone is sitting on the throne of the Underworld next to her husband Hades, her mother Demeter mourns and no longer gives fertility to the earth. This became an ancient Greek explanation for the seasons.