Toriel saves you from Flowey, and helps you in the first puzzle of the game. She leaves afterwards, to get her house ready for your arrival.
Toriel was married to Asgore, the original king of the monsters. But, after releasing everyone with Frisk, Asgore lost his power, and started dying. Pupi replaced him. Toriel then closed the underground again, making the Monsters trapped. But then, some years later, Chisp fell down, and Toriel took the advantage to take care of them.