A Varaha is a boar and the boar incarnation is usually catalogued as the third of Vishnu’s ten incarnations.
When the universe was submerged in water after the destruction that came at the end of padma kalpa, Vishnu slept on the waters. Thus he slept for a thousand mahayugas. Since the word nara means water and ayana means resting-place, Vishnu is also referred to as Narayana.
Brahma decided to start creation afresh, but discovered that the earth was submerged in water. How would his creations survive if there was no earth? He therefore requested Vishnu to bring the earth up from under the water.
Vishnu adopted the form of a boar and went to the underworld. He discovered the earth there and raised her up on the tusks of the boar. The boar carefully raised the earth and laid her to rest on top of the water. The earth began to float like a gigantic boat.
Since Vishnu raised the earth in the form of a boar at the beginning of the kalpa, the present cycle is known as Varaha kalpa.
(The story of the boar incarnation is rather summarily disposed of in the Kurma Purana. The other Puranas describe it at great length. Apart from the question of raising up the earth from under the water, the story revolves around the demon Hiranyaksha. This demon was the son of the sage Kashyapa and his wife Diti. He defeated the gods and drove them out of heaven. In desperation, the gods started to pray to Vishnu. Hiranyaksha used to live under the water and Vishnu entered the water in his form of a boar and killed Hiranyaksha. He also recovered the Vedas which had been stolen by Hiranyaksha.)