Dasara, also called as Vijaya dashmi, is a famous Hindu festival celebrated on the Dashami of Ashvin month. According to Hindu mythology people celebrate this festival because Goddess Durga killed demon Mahishasura on this day.
Once there lived a demon by the name of Mahishasura. He performed great penance for Lord Brahma for thousands of years. Lord Brahma pleased with his penance appeared before him and granted him a boon. Mahishasura asked that only a lady should be able to kill him and the birth of the lady should not be a natural birth. She should have enormous power and should be more powerful than the Trimurtis.
With this boon Mahishasura attacked all the worlds. He defeated Indra and took over the heaven. He made all the Gods his slaves and was torturing them. He did not leave humans, Rishi (sages) and was creating havoc in all the worlds.
All the Gods went to Brahma, Vishnu and Shiva. Gods asked Trimurti to help them in killing the demon. Knowing the boon given to Mahishasura that only a lady can kill, Trimurtis created a lady with all the power they had and she was none other than Goddess Durga. She took a Tiger as her vehicle. All the Gods gave their weapons to her and prayed to her to save them and the worlds from Mahishasura.
Goddess Durga, fought with Mahishasura for nine days and killed him on the ninth day. The day is celebrated as Maha Navami and Goddess Durga is worshipped as Mahishasura Mardini. The tenth day was celebrated by the world as it was freed from the clutched of the demon Mahishasura. The tenth day was called Dasara.