The Hymn gives Demeter's arrival at Eleusis a specific domestic scene rather than a general appearance. Disguised as an old woman, she is found sitting at the well by the daughters of Keleos, the local ruler, who bring her home and offer her a position nursing their infant brother Demophon. Demeter accepts, and secretly begins trying to make the child immortal, anointing him with ambrosia and placing him in the hearth fire by night to burn away his mortality, a practice that is going to plan until the boy's mother Metaneira spies on the ritual one night, cries out in fear, and interrupts it. Demeter, furious at the interruption and at mortal ignorance more broadly, drops the disguise, reveals her full divine form, and rebukes the household before turning her attention back to securing her own temple at Eleusis and the return of her actual daughter.
The episode does specific narrative work beyond decorating the goddess's grief. It stages, on a small human scale, the same theme the larger Persephone story stages cosmically, an attempt to defeat death interrupted by mortal limitation, and it explains why Eleusis in particular received the goddess's temple and her rites rather than any other place she might have passed through. The Hymn treats Demophon's failed immortalization and Persephone's own partial return, permanent but incomplete, as versions of the same lesson about what mortals, and even a grieving goddess, can and cannot ultimately secure.