The story behind the name and appearance of this Avatar concern's a sage's son, Rama, who became a brilliant archer. In gratitude for having this skill conferred on him he went to the Himalayas and did penance to Shiva for many years. Shiva was pleased with this devotion and, when fighting broke out between the gods and demons, ordered Rama to go and defeat the demons. Rama successfully did so. As a reward, Shiva gave Rama many gifts and weapons; one of these was a magnificent axe (parashu) after which Rama was known as Parashurama, and another was a bow. It is these two weapons he is shown carrying in his traditional iconography, as shown in the present artwork.
According to another story the incarnation of Parashurama was undertaken by Vishnu for the purpose of exterminating the Kshatriya, or warrior caste, which had tried to assert its authority over the Brahmanical. Twenty-one times Rama is said to have cleared the earth of Kshatriyas, but by various means some few were preserved alive who were able to perpetuate the race. The origin of this feud lay in the episode when a king stole the wish-fulfilling cow of Parashuram's father. Parashurama, who had once demonstrated his filial piety by beheading his own mother at his father's request and then having her brought to life again, took his revenge for the theft by killing the king. In return the king's son killed Parashurama's father. Thus Parashurama swore revenge by vowing to exterminate all of the ruling class, namely the Kshatriyas, from the face of the earth.
This description by Nitin Kumar, Executive Editor, Exotic India.
Danielou, Alain. The Myths and Gods of India: Vermont, Inner Traditions International, 1991.
Jansen, Eva Rudy. The Book of Hindu Imagery, The Gods and their symbols: Holland, Binkey Kok Publishers, 1998.
Mitchell, A.G. Hindu Gods and Goddesses: New Delhi, UBS Publishers, 1998, Eleventh Edition. Wilkins, W.J. Hindu Mythology: New Delhi, Rupa and Co., 1986.