Significance
Sharad Navratri is the most celebrated of the year's four Navratris — nine nights devoted to Goddess Durga in her nine forms (Navadurga), celebrating the triumph of the divine feminine (Shakti) over the demon Mahishasura.
It culminates in Vijayadashami (Dussehra), the day of victory.
The four Navratris
The year has four Navratris: the two great ones — Chaitra (spring) and Sharad (autumn) — and two Gupt (secret) Navratris in Magha and Ashadha, kept mainly by tantriks and dedicated sadhaks. Sharad Navratri is the grandest.
The nine days and nine goddesses
Each day worships a different form of Durga: Shailputri (Pratipada), Brahmacharini (Dwitiya), Chandraghanta (Tritiya), Kushmanda (Chaturthi), Skandamata (Panchami), Katyayani (Shashthi), Kalaratri (Saptami), Mahagauri (Ashtami) and Siddhidatri (Navami).
Rituals
The festival begins with Ghatasthapana (Kalash sthapana) and the sowing of barley. Many devotees fast, and evenings resound with Garba and Dandiya. Kanya Pujan (worship of young girls) is performed on Ashtami/Navami.
How the dates are fixed
Sharad Navratri runs nine consecutive nights from the Pratipada of Ashwina Shukla paksha to Navami; the Ghatasthapana muhurat is set on the first day for your location. The list above shows all nine days with the goddess worshipped each day.