An avatar of the Hindu deity Vishnu, Varaha takes the form of a boar and is the third of his ten worldly incarnations, collectively known as the Dashavatara (Sanskrit for ‘ten avatars’). These incarnations — Matsya (‘fish’); Kurma (‘tortoise’); Varaha (‘boar’); Narasimha (‘man-lion’); Vamana (‘dwarf’); Parashurama (‘Rama with an axe’); Rama or Ramachandra; Krishna; Buddha or Balarama; and Kalki (the avatar yet to come) — are widely associated with Vishnu’s role as the protector of humankind. Another belief is that the Dashavatara are the result of a curse laid upon Vishnu by Shukra — guru of the asuras, or demons — or the latter’s father, the sage Bhrigu. Vishnu’s form as Varaha is symbolically associated with power, wisdom and prosperity. 

In texts from the Vedic period (c. 1500–500 BCE) such as the Shatapatha Brahmana and Taittiriya Samhita, Matsya, Kurma and Varaha are avatars of the god Prajapati, assumed responsible for the creation of the world and its safeguarding. A form of the creator deity Brahma, Prajapati is equated with Vishnu and his incarnations in later texts such as the Puranas. In the Shantiparva book of the Mahabharata (compiled 300 BCE–400 CE), Varaha is one of six avatars of Vishnu; in other variations of the text he is listed as one of ten. The Bhagavata Purana lists him as one of twenty-two. 

The Taittirya Samhita is one of the earliest texts containing the Varaha myth. It tells that the universe was once composed of endless water, with the earth submerged below. Prajapati roamed the universe as a wind — spotting the earth as a lump of clay underwater, he assumed the form of a boar to retrieve it, and then became Vishwakarma, the divine architect, to expand and render its surface. The Shatapatha Brahmana tells a similar story, but refers to the boar as Emusha, his name from the early Vedic period. The Padma Purana (broadly dated between the fourth and fourteenth centuries CE), which has large sections dedicated to the myths of Vishnu, elaborates further on the story, personifying the drowned earth as the goddess Bhudevi abducted by the golden-eyed asura Hiranyaksha. Vishnu appears as Varaha, slays Hiranyaksha and lifts Bhudevi out of the water, bearing her on his tusks; she then becomes one of his consorts. Versions of this myth are also mentioned in several other Puranas, in which Varaha becomes more firmly identified with Vishnu than with the older Vedic figure of Prajapati. Some scholars have pointed out that the cosmogonic motif of the diving boar also appears in folk narratives of Indigenous peoples such as the Mundas of Orissa and the Koyas who are spread across eastern and central India. As such, the Varaha myth may be a variant of a creation story from older, pre-Vedic cultures.

The iconography of Varaha varies in textual sources: in some he is shown in his anthropomorphic form with the head of a boar and the body of a man, and others show his zoomorphic form with the head and body of a boar. Sculptures of Varaha depict him in both forms, though more often in the former than in the latter. His complexion varies from white to deep blue-black. He is often described as having four arms — two holding a shankha or conch, and two holding a chakra or discus. Other sources such as the sixteenth-century treatise Shilparatna mention the gada or mace and padma or lotus as objects in his grasp. The serpent Adishesha appears at his feet, and his wife Bhudevi stands by his side or sits on his right leg; in the Agni Purana, broadly estimated to date between the seventh and twelfth centuries CE, the goddess Lakshmi also appears as his consort. These motifs — the shankha, the chakra, the padma and Adishesha — are commonly associated with Vishnu and his various manifestations. One sculpted Varaha panel from Mamallapuram (or Mahabalipuram) shows the deity flanked by Brahma and another figure that some scholars believe to be Shiva.