Durga Puja is the Ashwamayadha Yagya of this day and age. But it's also very ancient. It goes all the way back to the Vedas. In Rig Veda, she reveals herself as the very existence of the universe. So that's the source of the idea of durga.
On the auspicious occasion of Durga Puja, Swami Sarvapriyananda speaks on the significance of the Divine Mother.