Navratri is one of the major festival celebrated in India. Typically it is celebrated for 9 nights and on 10th day it is celebrated as Vijayadashami or Dasera or Dashera or Dussehra. Vijayadashami literally means victory on the tenth lunar day. It is believed that goddess Durga fought with demons for 9 nights and 10 days. On this 10th day, she killed the demon Mahishasur.

Goddess Durga

Goddess Durga Killing Demon Mahishasur

Vijayadashami also signifies the victory of King Lord Rama over Ravana – the king of Lanka, who had kidnapped Rama’s wife Sita. In the epic Ramayana it is said that Rama got blessings from goddess Durga with knowledge of the way to kill Ravana. As per the hindu calendar, the day when Rama defeated Ravana was Ashvin shukla Dashami. As the day was 10th day it is celebrated as Vijayadashami.

Lord Rama killing Ravana

Lord Rama killing Ravana

On this day, today a big statue of Ravana is set on fire. After this defeact of Ravana, Lord Rama, his Brother Lakshmana and wife Sita, returned back to their kingdom of Ayodhya after 20 days of vijayadashami. Hence the festival of Diwali or Deepavali is followed after 20 days of Vijayadashami.
It was believed that Ravana had 10 bad qualities which was represented by him having 10 heads.

1. Kama vasana (Lust)
2. Krodha (Anger)
3. Moha (Attachment)
4. Lobha (Greed)
5. Mada (Over Pride)
6. Matsara (Jealousy)
7. Swartha (Selfishness)
8. Anyaaya (Injustice)
9. Amanavta (Cruelty)
10. Ahankara (Ego).

Vijayadashami can also be seen as victory over these 10 bad habits.

Source : http://en.wikipedia.org/wiki/Vijayadashami