Dussehra (Vijaya Dashami, Dasara, or Dashain) is a Hindu festival that celebrates the victory of good over evil. It is a "gazetted" holiday in India, which is marked on the 10th day of the bright half (Shukla Paksha) of the month of Ashvin (Ashwayuja). The festival actually falls on Sunday (10/13) this year, so Monday is a day off for us.
Many people of the Hindu faith observe Dussehra through special prayer meetings and food offerings to the gods at home or in temples throughout India. They also hold outdoor fairs (melas) and large parades with effigies of Ravana (a mythical king of ancient Sri Lanka). The effigies are burnt on bonfires in the evening.
As near as I can tell, there are only three national holidays in India: Republic Day, Independence Day and Gandhi's Birthday. Beyond these, the multi-cultural nature of India makes celebration of religious festivals a very complex and time consuming task. There are at least seven major religions - all with dozens of celebrations. Frequently, these are observed on a regional basis.
"Gazetted" seems to mean "mandatory" but subject to change. There are 14 of these, which are celebrated across all of India. The government determines specific holidays for its employees. Many other institutions (schools and banks, etc.) follow its lead.