You probably noticed that the myth of Persephone, Demeter, and Hades is an origin story – it's used to explain the origin of the seasons, and why food crops don't grow in the winter. When Persephone is in the underworld with Hades, Demeter refuses to let any plants grow. When Persephone is in the world of the living with Demeter, the earth and plants return to life.
Demeter is the goddess of agriculture, which is why she can mess up the growing season for all of us humans. If we take a step away from the seasons and think instead about seeds and crops, we can see the myth as the allegory for the planting seeds. Persephone is like a seed. Each year she must go under the earth, but she's reborn again in the spring when she returns to the world of a living. This is exactly what happens to a seed: it's planted underground, and then it sprouts in the spring.
Demeter, who was called Ceres by the Romans (like cereal), was most closely related to crops of grains. That's why in his telling of this myth, Thomas Bulfinch, of Bulfinch's Mythology fame, says:
There can be little doubt of this story of Ceres [Demeter] and Proserpine [Persephone] being an allegory. Proserpine signifies the seed-corn which when cast into the ground lies there concealed—that is, she is carried off by the god of the underworld. It reappears—that is, Proserpine is restored to her mother. Spring leads her back to the light of day.
We agree, but don't be fooled: Greeks and Romans didn't have any corn. Last we checked, corn didn't make it to Europe until after Columbus landed in the Americas in the late 1400s. In your mind, just imagine he's talking about wheat, or some other grain.