Demeter

"I understand, young Zagreus, that you would seek to leave that bitter darkness for this bitter cold? Quite honestly I fail to see why. But I'll aid your plight, why not? For I can offer plenty of assistance, and you soon shall grow fond of it, I think." Demeter is the goddess of agriculture as well as sacred law and the cycle of life and death, the giver of life and in turn, the taker of it.

Many of the boons she offers to Zagreus inflict her signature Status Curse, Chill, which causes enemies to slow down and, possibly, shatter, spreading the Curse. In addition to that, she offers the 2nd highest raw percentage damage increase. Her other boons vary between helping survivability by healing, increasing damage, or boosting your different boons over time by increasing their rarity.

Demeter boons excel at control, as Chill slows them down the more Zagreus strikes them. Since Chill is easy to stack and maintain, this also enables good synergy with the Mirror of Night Upgrade, Privileged Status.

Demeter only appears after reaching the surface for the first time (just reaching the final boss, they don’t have to be defeated), making her one of the three Olympian gods (the other two being Aphrodite and Zeus) who will not appear in the very first run of a save.

Affinity
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.

Favor
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.

Quotes
"For quotes and dialogue regarding Demeter, please refer to Demeter/Quotes."

Mechanics
Demeter boons mostly revolve around Chill and upgrading your Cast effects.