yada yada hi dharmasya glanir bhavati bharata
abhyutthanam adharmasya tadatmanam srjamy aham
paritranaya sadhunam vinasaya ca duskritam
dharma-sansthapanarthaya sambhavami yuge yuge
Source: Shreemad Bhagavad Gita, Chapter 4, Verse 7-8
Purport
“Oh descendant of Bharata, whenever and wherever there is a decline in religious practice and a predominant rise of irreligion, at that time I incarnate Myself. To protect the pious, vanquish the miscreants, and re-establish the principles of religion, I manifest Myself in every era.”
Dashavatar refers to the ten primary incarnations of Lord Maha-Vishnu. Of the ten: five appeared in Satya Yuga, two in Treta Yuga, two in Dwapara Yuga, and three in Kali Yuga.
The Ten Divine Incarnations
Avatar 1
Matsya Avatar
Satya Yuga
The Fish incarnation. Lord Maha-Vishnu saved the Vedas from the demon Hayagriva and guided Manu's ark through the great deluge, preserving all life and knowledge.
Avatar 2
Kacchapa / Kurma Avatar
Satya Yuga
The Tortoise incarnation. Lord Maha-Vishnu supported Mount Mandara on His back during the Samudra Manthan (churning of the cosmic ocean) to produce the nectar of immortality.
Avatar 3
Varaha Avatar
Satya Yuga
The Boar incarnation. Lord Maha-Vishnu plunged into the cosmic ocean, killed the demon Hiranyaksha, and lifted the Earth on His tusks, restoring balance to the universe.
Avatar 4
Narasimha Avatar
Satya Yuga
The Half-Lion Half-Man incarnation. Lord Maha-Vishnu emerged from a stone pillar to protect His devotee Prahlad, killing the tyrannical Hiranyakashipu at twilight — neither inside nor outside, on the Lord's lap.
Avatar 5
Vamana Avatar
Satya Yuga
The Dwarf incarnation. Lord Maha-Vishnu appeared as a dwarf Brahmin boy, then grew to cosmic proportions, covering all three worlds in two steps. With the third, He pushed King Bali into the underworld.
Avatar 6
Parashurama Avatar
Treta Yuga
The Warrior-Sage incarnation. Lord Maha-Vishnu took the Parashurama Avatar with an axe in hand and eliminated the oppressive Kshatriya clan from Earth 21 times to restore Dharma.
Avatar 7
Rama Avatar
Treta Yuga
Maryada Purushottam — the ideal king. Lord Rama killed the demon king Ravana, freed Sita from captivity, and established righteous rule (Rama Rajya), assisted by Lakshmana and Hanuman.
Avatar 8
Balarama / Haladhar Avatar
Dwapara Yuga
The Plow-bearer incarnation. Lord Balarama wielded the divine plow as His weapon and played divine pastimes alongside Lord Krishna, changing the course of the Yamuna River.
Avatar 9
Buddha Avatar
Kali Yuga
The Compassionate incarnation. Lord Buddha appeared in Kikata (Odisha) to oppose rampant animal sacrifice in Vedic rituals and re-establish the compassion of Sanatan Dharma.
Avatar 10
Kalki Avatar
Kali Yuga (Present)
The Final incarnation. Lord Kalki will appear in fierce form to destroy the wicked Mlecchas, establish righteousness for Satya Yuga, and reveal His identity to fervent devotees. He has already incarnated.
The Kalki Avatar — The Final Incarnation
athasau yuga-sandhyayam dasyu-prayesu rajasu
janita visnu-yasaso namna kalkir jagat-patih
Source: Shreemad Bhagavat Mahapurana, Canto 1, Chapter 3, Verse 25
mleccha-nivaha-nidhane kalayasi karavalam
dhumaketum iva kim api karalam
kesava dhrita-kalki-sarira jaya jagadisa hare
Source: Geeta Govinda, Poet Jaidev Goswami
Purport
In Kali Yuga, Lord Kalki will manifest in a fierce form, holding a large sword, riding a horse, destroying the wicked, and establishing righteousness for the upcoming Satya Yuga.