Demeter gives boons that add Chill to abilities, improve healing, and various debuffs.
If given Nectar, Demeter will give you the Frostbitten Horn.
Demeter's affinity gauge is maxed out at 7 hearts, requiring the gifting of 6 Nectar and 1 Ambrosia.
Demeter's favor requires completing the Epilogue, then a few instances of dialogue with her. The favor is completed when Demeter requests Zagreus to "be more candid with her" next time.
While it is not possible to forge a bond with Demeter before the Epilogue is completed, maxing out her affinity gauge to the locked heart will count towards the requirements to trigger the Epilogue.
Demeter boons mostly revolve around Chill and upgrading your Cast effects.