Durga Puja or Navratra/Navratri is a symbol of victory of good over evil. It is a festival for worshipping Durga Devi n her nine forms. It is celebrated to worship the victory of Devi Durga over Mahishasur.
In India every festival has a legend/ story behind it. Story behind celebration of Durga Puja is as follows:
Long before the Ramayan and Mahabharat Yug (era), there was a king of Demons (Asurs) known as Rambha. He was a devotee of Agni Dev (Lord of Fire). He worshipped Agni Dev. Agni Dev was happy with his penance and granted him a wish. He asked ” No God, no demon and no man would be able to kill me”. He was granted the wish. Rambha thought he had become invincible. So he went on to conquer all the three Loks (world)- Dev Lok, Prithvi Lok and Patal Lok.
Enroute his pursuit he fell in love with a she- Buffalo (Mahisi in Sanskrit). The buffalo was actually princess Shyamla who was cursed to live in the form of a buffalo. They both got married and Shyamla became pregnant.
One day Rambha go into a fight with another buffalo and was killed by him (as buffalo is neither God, man or demon). Shyamla decided to go Sati on the funeral pyres of Rambha. Because of Agni Dev’s blessing out of the pyre a human child having the head of the buffalo was born. He was the son of a Mahisi and Asur and so was named Mahishasur.
Because of Agni Dev’s blessings Mahishasur was powerful from the very beginning. He was more cruel as compared to his father Rambha. He yearned for mortality. So he started worshipping Lord Brahma day and night. (Some legends say that he worshipped Lord Shiva. People in go by either of the legend depending on their beliefs).
Lord Brahma was pleased by Mahishasur’s penance and granted him a Vardaan (wish). Mahishasur asked for immortality but Lord Brahma refused him saying that it was not possible. However he granted the Vardaan that Mahishasur could only be killed by a woman.
Mahishsur was pleased that he had tricked Lord Brahma into giving him immortality because he never thought that a woman could kill him. He began his conquest of the three Loks. After having captured Prithvi Lok and Patal Lok he started towards Dev Lok. He wrecked havoc there and threw away Lord Indra ( the king of Gods ) from his throne. He then declared himself as the King of the Dev Lok.
So all the Gods fled to Vaikunth Lok (the place of Lord Vishnu) and sought help from the Trimurti (Brahma, Vishnu and Mahesh(Shiv)). Lord Vishnu said ” Beacause of the wish granted by Lord Brahma Mahishasur cannot be defeated by any Man or Dev. We must all combine our powers and create a Devi (Godess) who will kill Mahishasur.” Hearing this all the Gods combined their powers. A beautiful light eminated from all the Gods which took the form of a beautiful Godess rightly known as “Durga”, the power of the universe.
After being equipped with all the powers and weapons , devi went ahead to fight Mahishasur. It is also said that Mahishasur fell in love with Devi and proposed to marry her. Devi Durga agreed but on one condition that he should defeat her in battle. So a fierce battle began between the two. The battle lasted for long. Finally Devi killed Mahishasur with her Trishul (Sword) and restored peace in all the Loks.
Some variations of the legend are also prevalent. But this is the legend that is believed widely throughout India.