Dussehrah is celebration of the victory of Good over Bad. Celebration of destruction of evil demons like Ravana and resurrection of peace and happiness to humanity.
The demons used to harass good people and prevent performance of yagas and yajnas for betterment of human life on earth. They engaged in forcing people to worship the demon kings in place of God. They killed people disobeying them and destructed the whole creation of God to establish their rein on earth and heaven. So God had to come to their rescue in the form of LOrd Rama and destroy Ravana and other demons to establish peace and happiness.
So, to commemorate this destruction of evil, this festival is being celebrated as Vijaya Dashami meaning Victory Day (tenth Day). It is celebrated for ten days to celebrate joy and express thanks to God and Goddess in their various forms.