In ancient times, the demon Mahishasura performed severe penance and obtained a boon from Lord Brahma that no god or demon could defeat him. Empowered by this boon, he conquered the three worlds — Swarga (heaven), Prithvi (earth), and Patala (netherworld) — and drove the Devas from heaven.
The Devas, humiliated and helpless, approached the Holy Trinity — Brahma, Vishnu, and Mahesh (Shiva). Enraged at Mahishasura's tyranny, the three gods combined their divine energies (tejas). From this blazing light emerged Maa Durga — a supreme goddess of incomparable power and beauty.
Each deity bestowed upon her their most powerful weapon: Shiva gave the Trishul (trident), Vishnu the Sudarshan Chakra, Brahma the Kamandal and Vedas, Indra the Vajra (thunderbolt), Varun the Shankh (conch), Agni the Shakti (spear), Vayu the bow and arrows, Vishwakarma the axe and armour, and Himalaya the lion as her divine mount.
Thus armed with divine weapons and riding her fierce lion, Maa Durga challenged Mahishasura. A terrible battle raged for nine days and nine nights. Mahishasura kept changing forms — buffalo, lion, elephant, warrior — to confuse the Goddess.
On the tenth day (Vijayadashami / Dashami), as Mahishasura took the form of a great buffalo, Maa Durga leapt onto him, pinned him with her foot, and pierced his chest with the Trishul, ending his reign of terror. The heavens rejoiced, the Devas showered flowers, and Dharma was restored.
This is why the nine nights are called "Navratri" (नव = nine, रात्रि = nights) and the tenth day is celebrated as Vijayadashami (Victory Tenth).