Once upon a time, there was a family of elemental dragon demons, led by one called Gogyou. After his wife's death, he fell into an altercation with a Dog Demon named Inu no Taisho. Eventually, Inu no Taisho won over Gogyou, killing the Dragon Demon, and leaving the eldest of his children - Faia and Mizu - to care for their two younger siblings - Ea and Koudo - on their own. Many years passed, and now, they are no longer children. Furious that their father was taken from them, the four Element Dragon Demons decide to seek revenge on the sons of the Dog Demon who killed their father - Sesshoumaru, and his half-demon half-brother Inuyasha.
Read a more detailed plot here: here.