The Varaha Avatar in the shape of a boar (varaha means boar), is the third incarnation of Vishnu, and belongs to the Satya yuga. The legend behind this Avatar is as follows:
Once it so happened that golden-eyed (Hiranyaksha) demon threw the earth to the bottom of the sea. Vishnu taking the form of a boar, jumped into the sea and rescued the earth. He then reestablished it, floating over the ocean like a large ship. Further he adorned it with mountains and then divided it into seven continents. In this way the world was brought into being once again.
On a symbolic level the boar incarnation is described as sacrifice personified; his feet being the Vedas, his tusks the sacrificial posts to which the victim is tied; his teeth, the sacrificial offerings; his mouth, the altar; his tongue, the fire; his hairs, the sacrificial grass; his eyes, day and night; his head, the place of Brahma; his mane, the hymns of the Vedas; his nostrils, all the oblations; his snout, the ladle of oblation; his voice, the chanting of the Sama-veda; his body, the hall of sacrifice; his joints, the different ceremonies; and his ears as having the properties of voluntary and obligatory rites.
Here he is shown symbolically holding the globe on his tusks, as he the savior of the earth.
Danielou, Alain. The Myths and Gods of India: Vermont, Inner Traditions International, 1991.
Garrett, John. A Classical Dictionary of India: Delhi, Low Price Publications, 1996.
Harshananda, Swami. Hindu Gods and Goddesses: Madras, Sri Ramakrishna Math, 1987.
Mitchell, A.G. Hindu Gods and Goddesses: New Delhi, UBS Publishers, 1998, Eleventh Edition.