Varāha-avatāra is the third among the Daśāvatāra. When Brahmājī was ordered to carry out the creation, he began to think about the details involved in the task. At that moment, a male named Svāyambhuva Manu and a female named Śatarūpā manifested from his body. Abiding by the desire of Brahmā, Svāyambhuva Manu accepted Śatarūpā as his wife in order to carry out the process of creation. Seeing the earth submerged in the waters of annihilation and desiring to seek a dwelling place for the living beings, Manu approached his father, Lord Brahmā, and prayed to him to rescue the earth. When Brahmā saw the earth submerged in the water, he thought for a long time about how it could be rescued. He had earlier established the earth in its normal state after removing all the water, but could not understand why the earth had again sunk into the watery abyss. He had been appointed to do the work of creation but the earth had become inundated in a deluge and had sunk into the depths of the ocean to Rasātala (the lowest of the seven underworlds). How was the act of creation to be accomplished? How was the earth to be rescued?

Lord Brahmā could not think of a solution even after much thought and effort. At last, he took shelter of the Supreme Lord, Viṣṇu. While Brahmā was still deep in thought, a small boar the size of a thumb suddenly appeared from his nostril. Astonishingly, as Brahmā looked on, the tiny boar expanded in the sky and within moments had assumed a form as large as a great elephant. Brahmā, great brāhmaṇas such as Marīci, the Four Kumāras (Sanaka, Sananda, Sanātana and Sanat-Kumāra) as well as Svāyambhuva Manu, saw the transcendental Varāha form and began to discuss this wonderful event. Lord Brahmā thought that this must be some resident of the transcendental world travelling in disguise in the form of a boar. “Oh! What a great surprise! How wonderful it is that this expanding Varāha form has come forth from my nostril. Is Śrī Hari, the lord of sacrifice, concealing His original form and trying to agitate me?”

In this way, while Brahmā was deliberating with his associates, Śrī Hari roared tumultuously like the great mountain Girirāja. The omnipresent Śrī Hari enlivened Brahmā and the other highly elevated brāhmaṇas by again roaring with His uncommon voice. The sound of His roar was so sweet that it would destroy all the miseries of the hearer. Lord Brahmā, Svāyambhuva Manu and other sages who reside in Janaloka, Tapaloka and Satyaloka, chanted auspicious mantras from the Vedas as offerings to Varāhadeva. Upon hearing the prayers of Brahmā and the other sages, Lord Varāha prepared to enter into the waters of annihilation for the benefit of the demigods. Lord Varāha rose into the sky while slashing His tail. The Lord quivered the hair on His shoulders and scattered the clouds in the sky with His hooves. With raised hairs, white tusks and luminous effulgence, the Lord’s form was brilliantly beautiful. This is a unique and wonderful pastime of Śrī Hari. Just the remembrance of it causes shivering in the body. Despite being omnipotent and omniscient, He searched for the earth planet in the way that an animal would, using the sense of smell. Although His external appearance was fearful, He pleased the sages engaged in offering prayers by lovingly glancing over them and entering into the water. His dive into the water with His thunderbolt-like mountainous body divided the ocean. The ocean prayed to the Lord out of fear, “Please protect me, O Supreme Lord!”

The Lord of all sacrifices separated the water with His hooves and saw the earth lying at the bottom of Rasātala in the same way as when He had carried her in His stomach during the time of annihilation. Appearing very splendid, Lord Varāha lifted the earth by carrying her on His tusks. At that time, a very powerful demon named Hiraṇyākṣa challenged the Lord with a mace. Lord Varāha expressed great anger upon seeing the demon. Thereafter, Lord Varāha killed Hiraṇyākṣa just as a lion kills an elephant, and the cheeks and face of the Lord became red with the blood of the demon¹. With folded hands, the sages headed by Brahmā offered prayers to the Lord. The Lord, being satisfied with the prayers of the great sages, placed the earth upon the turbulent water with His hooves and then disappeared from their vision. There is a very important point to understand here. The Laghu-bhāgavatāmṛta says:

“Lord Varāha appears twice in one day of Lord Brahmā. During the Svāyambhuva-manvantara, He appeared from Brahmā’s nostril and rescued the earth, and during the sixth manvantara (Cākṣuṣa-manvantara) He appeared to rescue the earth and kill Hiraṇyākṣa.”

According to the Laghu-bhāgavatāmṛta, in the lineage of Uttānapāda, the son of Pracetā was Dakṣa, the daughter of Dakṣa was Diti, and the son of Diti was Hiraṇyākṣa. At the time of the appearance of the original (ādi) Varāhadeva at the beginning of the kalpa, Manu did not have any sons or daughters. How then could Hiraṇyākṣa have taken birth during the Svāyambhuva-manvantara? Therefore, it is seen that in the Bhāgavatam, Maitreya Ṛṣi described the pastimes of Lord Varāha in both the Svāyambhuva-manvantara and Cākṣuṣa-manvantara at the same time. Svāyambhuva Manu and Śatarūpā gave birth to two sons: Priyavrata and Uttānapāda, and three daughters: Ākūti, Devahūti and Prasūti.

dvītiyaṁ tu bhavāyāsya rasātala-gatāṁ mahīm
uddhariṣyann upādatta yajñeśaḥ saukaraṁ vapuḥ
(Śrīmad-Bhāgavatam 1.3.7)

“For the welfare of the world, and due to the desire to rescue the earth which had fallen to Rasātala, the supreme enjoyer of all sacrifices accepted His second manifestation as a boar.”

Here, Lord Varāha is described as the second avatāra:

yatrodyataḥ kṣiti-taloddharaṇāya bibhrat
krauḍīṁ tanuṁ sakala-yajña-mayīm anantaḥ
antar-mahārṇava upāgatam ādi-daityaṁ
taṁ daṁṣṭrayādrim iva vajra-dharo dadāra
(Śrīmad-Bhāgavatam 2.7.1)

“The unlimitedly powerful Lord assumed the form of a boar for the rescue of the earth and pierced the first demon, Hiraṇyākṣa, with His tusk.”

jalakrīḍāsu ruciraṁ vārāhīṁ rūpamāsthitaḥ
adhṛṣyaṁ mānasapyanyair vāṅgmayaṁ brahma-saṁjñitam
pṛthivyuddharaṇārthāya praviśya ca rasātalam
daṁṣṭrayābhyujjahārai nā mātmādhāro dharādharaḥ
dṛṣṭvā daṁṣṭragravinyastāṁ pṛthvīṁ prathita pauruṣaṁ
astavan jana-lokasthāḥ siddhā brahmarṣayo harim
(Matsya Purāṇa 6.8-10)

“The Supreme Personality of Godhead who is imperceptible to the mind, who plays beautifully in the water and who is the Sound-God designated as Absolute Brahman, appeared as Varāha to save the life-giving earth. He entered into the depths of the ocean and rescued the earth with His tusks. Seeing the earth resting on the tusks of the Lord, the sages of Janaloka offered prayers to the most celebrated Śrī Hari.”

Here it is said that Lord Nārāyaṇa, the cause of creation and destruction, appeared as Varāha:

vasati daśana-śikhare dharaṇī tava lagnā
śaśini kalaṅka-kaleva nimagnā
keśava dhṛta-śūkara-rūpa jaya jagadīśa hare
(Śrī Jayadeva’s Daśāvatāra-stotra, 3rd Verse)

“O Keśava! O Supreme Lord, You have assumed the form of a boar! O Lord! The planet earth rested on Your tusk and it appeared like the moon engraved with spots.”

Brahmā offered prayers to the Supreme Lord, Śrī Kṛṣṇa, when He manifested in the womb of Devakī while she was in the prison of Kaṁsa. The following is the last verse of those prayers:

matsyāśva-kacchapa-nṛsiṁha-varāha-haṁsa-
rājanya-vipra-vibudheṣu kṛtāvatāraḥ
tvaṁ pāsi nas tri-bhuvanaṁ ca yathādhuneṣa
bhāraṁ bhuvo hara yadūttama vandanaṁ te
(Śrīmad-Bhāgavatam 10.2.40)

“O Supreme Controller, Your Lordship previously accepted avatāras as Matsya (fish), Aśvagrīva (horse), Kūrma (tortoise), Nṛsiṁhadeva (half man/half lion), Varāha (boar), Haṁsa (swan), Lord Rāmacandra (the son of Daśaratha), Paraśurāma, Vāmanadeva and other forms, to protect us and the three worlds (heaven, earth and underworlds). O Kṛṣṇa, best of the Yadus, we respectfully offer our obeisances unto You. Now, by Your mercy, please protect us again by diminishing the burden of sins in this world.”

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¹ - Seeing Varāhadeva within the water (Rasātala), the demon Hiraṇyākṣa misunderstood the Lord to be an ordinary boar. Considering Him to possess meager strength, he spoke many deriding words. The Lord, however, returned his taunts with equal vigour. Lord Varāha dodged the violent mace-blows of the angry demon Hiraṇyākṣa, and thus a violent mace-fight began between the two. Lord Brahmā prayed to the Supreme Lord to please kill Hiraṇyākṣa in the loka-saṁhāra-kāriṇī-saṅdhyā, in the auspicious period known as Abhijit (during the evening in conjunction with the Abhijit star—the time that would be the most favourable for the destruction of a demon). After that, during the demoniac hours, the powers of the demon would increase manifold.

Hiraṇyākṣa displayed his prowess by using the mace and trident, and finally by casting illusions and striking hard with his fists, but the Lord killed the demon by a severe kick. This pastime has been described in the Third Canto, Chapters 18 and 19, of Śrīmad-Bhāgavatam.