Final answer:
Demeter's name in Greek likely derives from 'earth' and 'mother', representing her as the Earth Mother. Her association with grain, agriculture, and fertility was central to her worship in ancient Greek religion, with significant political and social implications in cities like Megara.
Step-by-step explanation:
The name Demeter originates from the Greek language and is believed to comprise of the words 'de', likely a form of 'ge' meaning 'earth', and 'meter' or 'mother', essentially rendering the name Demeter's synonymous with 'Earth Mother' or 'Mother Earth'. This etymology reflects her role as a goddess of agriculture, grain, and fertility in ancient Greek religion. Her significance and worship were widespread across Greek cities, with Demeter's temples and festivities deeply rooted in the socio-political and agricultural practices of the time. The Thesmophoria, her major festival, celebrated her as a bringer of laws and civilization, linking her to the political power and the procreative force essential for the continuity of communities.
In Megara, Demeter was particularly important, underlining her connection with the city's foundation. The cult of Demeter in Megara and various other Greek cities indicates an old association of the goddess with political authority and her intrinsic role within the local pantheons. Even the epithets of Demeter, like Demeter Thesmophoros, reflect her significance and the variety of roles she played in the ancient societies.