From the Vijayadashami Wikipedia page:
Vijayadashami, also known as Dussehra or Ayudhapuja, is an important Hindu festival celebrated in a variety of ways in Nepal, Sri Lanka, India, Bangladesh and parts of Pakistan. "Dussehra" is derived from Sanskrit; Dasha-hara is a form of Dashanan ravan ("Ravana's defeat").
The day marks the victory of Durga over the demon Mahishasura. The goddess fought with evil for ten days and nine nights. "Vijayadashami" is derived from the Sanskrit vijaya-dashami (victory on the dashami: the tenth day of the Hindu month). Diwali, the Festival of Lights, is celebrated twenty days after Vijayadashami.