Durga came to Earth on the invitation and prayers of the people who were being harassed . She came down in her form of Mahisha Mardini or the slayer of the Buffalo which has ten hands holding ten different weapons given to her by the various Gods. She came riding her mount the Lion on the invitiation of her devotees. On the eighth day of the Sukla Paksha in the month of Ashwin she arrived on Earth.
On the ninth day the battle ensued with Mahishasura and the battle continued through the night.
The demon hid easily among Buffaloes by taking their form . But Durga cut off its head to reveal the Demon and eventually on the tenth day or on Vijay dasami she slayed Mahishasur with the help of her mount the Lion.
A brief of Mahishasura-Durga Battle
Armed with incredible powers, Maa Durga reached Alkapuri . Durga and her lion roared in unison. The roar shook the throne Mahishasura was sitting upon. The floor trembled. Mahishashur flew into rage. He called out to his chief commander, "Go and find out what that roar was!"
The commander and his demon soldiers departed and found Bhagwati Durga at the city gate. They asked who she was. Durga replied that she was the death for Mahishasur. She asked the commander to tell his master that he should vacate Indra throne and run away or get destroyed. The soldiers went back to the court and delivered the message of Durga to Mahishasur. Mahishasur rose up in fury and thundered, "Let me see the silly woman thing. Come."
Mahishasur arrived to face Durga with a large demon army. The sight of Durga surprised him. He said, "Dear beauty, those slender hands of yours are not for weapons. I am new Indra, Mahishasur. Marry me and rule the heavens. I promise to make you my principal queen."
The demon talk made Durga explode in anger. She roared her challenge, Mean demon! I come as your death, Take this!' Durga threw Her trident. The demon evaded it and guffawed. He shot fiery flames at Durga. Durga blew away the flames which fell on the demons turned into flamelets. The demons ran around to escape from the falling fire balls.
It annoyed Mahishasur....
Suddenly, Mahishasur transformed into a raging buffalo bull. He ran at Durga, spewing fire and digging off stones with his hooves.
Durga's lion roared and raised its paw. She charged with Her trident at the bull's neck. Mahishasur bull froze. Blood gushed out of his neck wound. He bellowed in pain.
The demon ran frightened.
After a short time, Mahishasur changed tactics. Giving up his bull form, he charged at Durga with sword. Durga countered with sword. He tried all his sorcery tricks. But Durga countered all his moves effectively.
Putting Mahishasur in quandary, Durga roared, Evil headed demon! You are only prolonging your death. You can't survive this battle. Today you shall die."
Now Mahishasur was really frightened. But he put on a brave face saying, " Mahishasur is a warrior. He does not hit women. I defeated all the gods and made them flee. How would you defeat me when all them could not? There is no warrior in the three worlds to vanquish me."
"Foolish demon!' Durga roared and reminded, " You forget what you asked for from Brahma. Let me bring back your memory. You had said that if some woman killed you it would not matter. You had thought that a member of the weaker sex would pose no challenge to you. Now you can see that the same Lord has sent a woman to put you death. So, you must die. Nothing can save you. I am born just to slay you. Now, pick up your arms and fight."
End of Mahishasur
Durga's reminder put a scare into the mighty demon. He made up his mind to fight to the finish.
The demon launched a fierce attack. As a bull buffalo he charged at Durga. Durga beheaded the bull with Her sharp edged trident. The demon head emerged out of the severed neck of the bull. Durga again used Her trident which went through the neck of Mahishasura. With a horrifying groan Mahishasura fell down like an uprooted tree. Hundreds of demons got crushed under him.
The gods showered flowers from the heavens. The conchshells were sounded in victory. The heavens celebrated it with divine illuminations.
Indra again descended on his throne. A greatful Indra prayed along with other gods, "O goddess Durga! Whenever gods or humans are in trouble do extend your protection just like you have done now."
Maa Durga said, "So be it," and then vanished.