The “Avatar” or divine descendent refers to the Supreme Lord taking a brief human form for his own purposes, which are considered to refer to the welfare of the world or universe, which is His own creation. Potentially, Jiva in every being is in the sense an Avatar, which is best expressed by the Mahavakya, Tat Tvam Asi.
“Paritranaya sadhunam vinashaya cha dushkritam.
Dharma sansthapanarthaya sambhavami yuge yuge…”
These lines are from Bhagvad- gita (4.8),
Which closely translate to
“For the up-liftment of the good and virtuous,
For the destruction of evil,
For the re-establishment of the natural law (Dharma),
I will come, in every age”…..
The avatars of Lord Vishnu appear in the Hindu mythology whenever the cosmos is in crisis or grave danger, typically because the evil has grown stronger and has thrown the cosmos to Imbalance or out of control.
The avatar then appears in a material form, to destroy evil and its roots, and restore the cosmic balance between the ever-existent forces of good and evil.
Lord Vishnu have so far (in this cycle of yugas) incarnated on earth 23 times, while the 24th avatar is yet to be known as ‘Kalki Avatar’. Out of these 24 avatars, 10 avatars, called as Dashavatar, are considered to be the main incarnations of Vishnu. This is Matsya avatar, Kurma avatar, Varaha avatar, Narasimha avatar, Vamana avatar, Parashuram avatar, Rama avatar, Krishna avatar, Buddha avatar and Kalki avatar. Of all the Avatars, Shri Krishna alone is considered a Purna Avatar (Swayam Bhagawan) , a direct and complete representation of the Supreme Divine Himself.
From Bhagavata Purâna, the 24 avatars are:
1. Varâha — In order to raise the Earth from the waters, the Purusha adopted the body of Varâha or Boar and killed with His tusks the first Daitya Hiranyâksha.
2. Yajna — was born of Ruchi and Âkuti. The Suyama Devas were born of Yajna. He dispelled the fears of Trilokî.
3. Kapila — was born of Kardama Prajâpati and his wife Devahûti. He taught Brahmâ Vidyâ to his mother.
4. Dattâtreya — He preached Yoga to his disciples, who acquired powers and became liberated.
5. The Kumâras. — Sanat Kumâra, Sanaka, Sanandana and Sanâtana. They completely promulgated the Âtmâ Vidyâ, which had been lost in Pralaya.
6. Nara Nârâyana. — They were born of Dharma and his wife Murti, daughter of Daksha. Their Tapas was so great that the Deva ladies could not shake it.
7. Dhruva. — Though a boy, he could not bear the words of his step-mother. He went into the forests and made Tapas. He was rewarded with ascent to Dhruva Loka or the region of the polar star.
8. Prithu. — He milked out riches and edibles from the earth.
9. Rishabha. — Rishabha was the son of Nàbhi by Sudevi or Meru Devi. He roamed about as Parama Hansa.
10. Hayagrîva. — This horse-headed Avatâra appeared in the Vedic Yajna and promulgated the Vedas.
11. Matsya. — Vaivasvata Mann found out this Avatâra at the end of a cycle of Yugas. He preserved all beings and the Vedas from the waters of the Deluge.
12. Kûrma. — At the great churning of the Ocean, the Tortoise Avatâra supported the Mandâra mountain.
13. Nrisinha. — The Man-Lion Avatâra killed Hiranyakâsîpu.
14. Hari — saved the Elephant King of the famous story of Gajendra Moksha.
15. Vâmana — measured the Trilokî by His two steps.
16. Hansa — related Bhakti Yoga, Gnana and Bhâgavata Purâna to Nârada.
17. The presiding deity of each Manvantara.
18. Dhanvantari — promulgated the science of medicine.
19. Parasu Râma — suppressed the Kshatriyas who became disregardful of the Brâhmanas and the Sâstras.
20. Râma — destroyed Lankâ and killed Râvana.
21. Krishna. — The tenth Canto of Bhâgavata is entirely devoted to His deeds.
22. Vyâsa. — He divided the trunk of the Veda tree into several branches.
23. Buddha. — When the Asuras came to know the Vedic mysteries and to oppress people, Buddha incarnated Himself in order to confound them by preaching a variety of by-religions.
24. Kalki — will appear before the end of Kali Yuga, to set things right.