On this day in the Treta Yug, Shri Ram, the seventh incarnation of Vishnu, killed the great demon Ravana who had abducted Rama's wife Sita to his kingdom of Lanka. Rama, his brother Lakshmana, their follower Hanuman and an army of monkeys fought a great battle to rescue Sita. Rama had performed "Chandi Homa" and invoked the blessings of Durga, who blessed Rama with secret knowledge of the way to kill Ravana. On the day of Ashvin Shukla Dashami, Rama's party found Sita and defeated Ravana. Thus it is termed as Vijaya Dashami.
Happy Vijaya Dashami!