The Fruit of the Underworld, colloquially known as a Pomegranate, was one of the most important fruits in Greek mythology. When Hades abducted Persephone in an attempt to make her his wife, he tempted her with Pomegranate seeds. By eating food of the Underworld, it ensured she would spend at least part of the year there with Hades. This is why the Pomegranate has come to represent temptation in Greek Mythology.
Near the end of Kratos' journey to find Calliope, he encounters Persephone, sitting near the Forsaken Tree. She speaks to Kratos, and picks a Pomegranate from the tree. This is a symbol of temptation, as Kratos is tempted to dispel his weapons in the vain attempt to see his daughter.