The victorious (vijaya) tenth (dashami) is celebrated on the tenth day of the bright phase of the moon in the month of Ashvina (September/October) in rememberece of
the victory of Rama over demon Ravana
and
the victory of Durga over demon Mahisha. Durga feighted 9 days, the 10th was the victory.
http://hindumythologyforgennext.blogspot.com/2011/12/goddess-durga-slayer-of-mahisha.html