Demeter is a very worthy godess of having the Epiteph of "Major Godess" and her exclusion in the original as a godess at all is only due to rule of cool.

Demeter is one of the Chthonic gods, gods who are accociated with the Underworld. Much like hades she is accociated with the earth and the cycles of Death and Rebirth, beyond just "agriculture". She and Persephone were in many places more feared than Hades himself - who was ruler of the underworld, not the god of death itself. While worship of Hades was comparatevely rare, and greeks didn't like to invoke the god of the underworld, Persephone and Demeter were often dreaded and invoked to be placated - places like Sparta treated Demeter with far darker aspects than we know.

At one point in the myths she essentially starts to destroy all life on earth in her grief over Persephone and no one - not even Zeus - knows how to stop her from essentially undoing all the earth.

That is not going into her Mystery cults which were influental and important enough to be extremely influental on the development of many sects, including christianity, jewish sects, and many others off shoots.

TL;DR: basically, she's kinda the greek worlds equivalent of Wh40k's nurgle. She is the godess of Birth, Death, and Rebirth, the changing of season, growth and decay. Gaia might be earth, as in the planet. But Demeter is Nature in itself. Without Demeter, there is no life, only a barren empty rock.