In Vedic philosophy avatar is a deliberate descent of a deity from heaven to earth, or a descent of the Supreme Being (i.e., Vishnu for Vaishnavites) and is mostly translated into English as "incarnation", but more accurately as "appearance" or "manifestation". The term is most often associated with Vishnu, though it has also come to be associated with other deities.
First of all the word avatara actually means a form of God when He descends into this material world. There are many such forms listed in the Vedic texts, which will be discussed in this article. Many times they are referred to as incarnations of God. But the word incarnation is not proper either because it actually means when someone or something reincarnates, or takes another material body of flesh and blood. However, people use the word incarnation in this context quite often anyway.
But God does not take such a material form. His form is always spiritual, transcendental to the norms and laws of material nature. And He descends from the spiritual strata as He is, or in a form to do a specific activity, mission, or carry out a particular purpose. For this reason, the Supreme has many names, according to His forms and activities that He displays in His cosmic creation.
1. Matsya, the fish-avatar who saved Manu – the progeniter of mankind from the great deluge and rescued the Vedic scriptures by killing a demon. Story can be found in the Matsya Purana.
2. Kurma, the tortoise-avatar, who helped in the Samudra manthan – the churning of the ocean. Story can be found in the Kurma Purana.
3. Varaha, the boar-avatar, who rescued the earth from the ocean, by killing her kidnapper-demon Hiranyaksha. Story can be found in the Varaha Purana.
4. Narasimha, the half man-half lion avatar, who killed the tyrant demon-king Hiranyakashipu, to rescue the demon's son Prahlada, who was a Vishnu-devotee
5. Vamana, the dwarf-avatar, who subdued the king Maha Bali. Story can be found in the Vamana Purana.
6. Parashurama, sage with the axe who killed the thousand-armed king Kartavirya Arjuna
7. Rama, the king of Ayodhya and the hero of the Hindu epic Ramayana
8. Krishna, the king of Dwarka, a central character in the Bhagavata Purana and the Mahabharata and reciter of Bhagavad Gita. However, in the original Dasavatara stotra, Balarama, the elder brother of Krishna, is stated as the eight incarnation, while Krishna (Lord Kesava) is the source of all the incarnation.
9. Gautama Buddha, Among the Dasavatara, Sri Buddha is the ninth avatara. In order to condemn the practice of animal sacrifice, Supreme Lord Vishnu appeared in the form of Buddha.
10. Kalki ("Eternity", or "time", or "The Destroyer of foulness"), who is expected to appear at the end of Kali Yuga. Story can be found in the Kalki Purana.
As many as forty specific avatars of Vishnu are mentioned in the Bhagavata Purana.
1. Four Kumaras – the four Sons of god Brahma and exemplified the path of devotion.
2. Varaha the Lord lifted the earth out of the ocean and battled Hiranyaksa.
3. Narada the divine-sage who travels the worlds as a devotee of Vishnu
4. Nara-Narayana – the twin-sages
5. Kapila – a sage and one of the founders of the Samkhya school of philosophy
6. Dattatreya – the combined avatar of the Hindu trinity Brahma, Vishnu and Shiva. He was born to the sage Atri became a great seer himself.
7. Yajna – the lord of fire-sacrifice, who took was the Indra – the lord of heaven
8. Rishabha – the father of King Bharata and Bahubali
9. Prithu – the sovereign-king who milked the earth as a cow to get the world's grain and vegetation and also invented agriculture
10. Matsya , he appeared to Manu and saved him from the flood.
11. Kurma , he supported the process of amrit-manthan.
12. Dhanvantari – the father of Ayurveda medicine and a physician to the Devas.
13. Mohini – the enchantress
14. Narasimha , he vanquished Hiranyakasipu to save Prahlada, his devotee.
15. Vamana , he was born to Aditi and brought out the humility in Mahabali.
16. Parashurama , he cleaned the earth of all Kshatriyas three times over.
17. Vyasa – the compiler of the scriptures – Vedas and writer of the scriptures Puranas and the epicMahabharata
18. Rama , he vanquished the Rakshasa Ravana.
19. Balarama - brother od Lord Krishna
20. Krishna , he participated in the Mahabharata and is the protagonist of many stories and parables.
21. Buddha in the beginning of Kali-yuga the Lord will appear as Lord Buddha, the son of Anjana, in the province of Gaya (Bihar) just for the purpose of infatuating those who are envious of the faithful demigods.
22. Kalki , he will incarnate at the end of the current Kaliyuga with Parashurama as his guru.
Besides these, another four avatars are described later on in the text as follows:
1. Prshnigarbha – the son of Prshni
2. Hayagriva – the horse-faced avatar
3. Hamsa – the swan, he expounded on the Vedas to Sage Narada.
4. Golden incarnation of the Supreme Lord as Shri Chaitanya Mahaprabhu who incarnated in Navadwip. Avatara in Kali-yuga for propagating hari-namasankirtan.