The goddesses Persephone and Demeter belong to an earlier phase of Greek religion and in fact may have originally been imported from Sumer. They were worshiped at Eleusis in Mycenaean times (the period before the Trojan War). They are agricultural goddesses who are emblems of the fertility of the land. Modern scholars believe that the rituals involved in worshiping these goddesses existed before stories were composed to explain the goddesses being worshiped. These stories, in the form of songs, were gradually incorporated into the rituals which honored the goddesses. As with many parts of Greek religions, stories about these two goddesses have been handed down in many different works including Hesiod's Theogony, the Homeric Hymn to Demeter, Diodorus Sicilus, Pausanius, and Claudian among other authors. Thus there is no single story "The Myth of Demeter and Persephone" but instead a complex and varied tradition of different accounts of these goddesses and the rituals performed in their honor.
The myths or stories about these two goddesses were attempts to explain how crops went underground in winter and were reborn in summer. Thus the main point is not entirely a moral one but one of death and rebirth.
The major moral point in the Homeric hymn is one concerning hospitality. A moral often drawn from this and similar tales is that one should always be kind and welcoming to strangers as they may be gods in disguise, walking among us as mortals. Another important moral found in Zeus' response to Demeter's pleas is that even the king of the gods is not above the law.
Finally, as we see in the end of the poem, the audience is reminded that the rituals of Demeter are sacred, celebrate the rebirth of grains after they have been underground, and the precise nature of the showing of the sheaf of grain and other elements of the ritual are not to be revealed to the uninitiated. This impresses on its audience the great powers and mysteries of the goddesses.