For the Greeks, Demeter is an earth goddess; her name is De, which means earth (the same word as Gaia) and meter, which means mother. Demeter is the goddess of growing things, especially of grains like wheat and barley and millet.
Demeter's daughter, Persephone, is the grain itself, so Demeter is the earth giving birth to the grain.
Mythologically, Demeter is the sister of Zeus, Poseidon, Hades, and Hera, and so, like them, she is the daughter of Gaia, or Earth. This makes a lot of sense for a goddess of growing crops, because that is exactly what produces crops: earth.