The Goddesses of Eternal Maidenhood (or TGOEM for short) are a group of sacred virgin goddesses, led by Hestia. Their members take a vow of chastity. They seek to be good role models and spend their lives serving others, largely by performing charity work.
TGOEM gave Persephone a scholarship for university in exchange for her appearing as their spokeswoman at a few events, and under the impression she would officially join the organization when she finished her training as a sacred virgin.
Hera appears to be annoyed that Hestia keeps recruiting new goddesses for TGOEM, as it makes it hard for Hera to do her job as Goddess of Marriage.