The story is very bare even moreso than the SNES games. But the plot is you reawaken as a half demon, half human, 100% f-kboi. The plot says you have the choice to remake the world, but after seeing everyone from the first 20 minutes of the game, you're just here to collect demons and fistfight with the devils of most major religions. See the origins of a new century for Atlus.
Warning, the first five hours is very tedious as the enemies don't give you much money and experience points but are a pain to fight. It's better to turn on Merciful difficulty because life is short and you have punching to do.