Mahisha is the buffalo-headed monster that was killed by Durga in her battle of the Gods with the asuras. The Demons had taken power from the gods as they defeated them in the battle. The demons controlled the priests and consumed the offerings which were made to gods. The gods were baffled by the power of demons and they created Durga from different parts of their body. Durga destroyed Mahisha and other Asuras.
According to Mhabharata, Mahisha was a monster who was killed by Skanda. The modern form of Mahisha is believed to be Bhainsasura, who lives in the cornfields and tramples the plants unless he is propitiated by an offering of a pig or is worshipped when the rice is ripening.