Significance
Dussehra, or Vijayadashami, celebrates the victory of good over evil — Lord Rama's slaying of the demon king Ravana, and Goddess Durga's triumph over Mahishasura. It concludes Navratri and Ramlila.
The day is considered highly auspicious for new beginnings, and marks the start of preparations for Diwali.
Rituals
Towering effigies of Ravana, Meghnad and Kumbhakarna are burnt at sunset to cheering crowds. Devotees perform Shami-puja and Shastra-puja, exchange the leaves of the shami/apta tree as "gold," and Durga idols are immersed.
How the date is fixed
Dussehra falls on the Dashami of Ashwina Shukla paksha, decided by the tithi's presence in the afternoon (aparahna), the traditional time of victory, so the aparahna muhurat is shown above for your location.