Lord Vishnu is the sustainer of the 'Thrimurthy'. And so to sustain peace and well-being,and to restore Dharma,He incarnates on earth in various forms and does the needful. To quote one of the most popular lines of the Bhagavad Gita...
Yada yada hi dharmasya
Glanir - bhavathi bharata
Abhyudhanam adharmasya
Tadathmaanam srijaamyaham
Parithraanaya cha saadhunam, vinaashaya cha dushkrithaam
Dharma samsthaapanaarthaaya sambhavaami yuge yugey...
The First Avatar - Matsya (Fish form)
Object of incarnation - To destroy the horse-headed asura (demon) called Hayagriva,and restore the sacred Vedas he stole from Brahma. Also guided the vessel filled with his devotee Satyavrata and other beings to safety as the Pralaya (tsunami)to signify the end of that Kalpa (a measure of time) ravaged Earth.
The Second Avatar - Kurma (Tortoise )
Object of Incarnation - To keep mount Mandhara from sinking into the Paalazhi (Ocean of milk), while the devas and asuras used the mountain as the churn and vasuki the serpent as rope. This was done to help the Devas (gods)regain their immortality by drinking Amrit (nectar) that could be churned up from the ocean. Vishnu also appeared as 'Mohini' to make sure that the evil Asuras would not get their share of Amrit.
The Third Avatar - Varaha (Wild Boar)
Object of Incarnation - During the Pralaya at the end of the Kalpa, Bhoomi Devi (mother earth) sank to the ocean bed. Lord Vishnu her back up,balanced on his snout. Also killed the Asura Hiranyaksha.
The Fourth Avatar - Nara-Simha (Half man-half lion)
Object of Incarnation- To destroy Hiranyakashapu,brother of Hiranyaksha who terrorises earth and heaven after getting a boon from Brahma that death would not come to him in the form of Man or beast, day or night, indoors nor outdoors, on earth or in the sky. And so Vishnu appears as Narasimha neither man nor beast. At the twilight hour (neither day nor night). He drags Hiranyakashapu to the threshold (neither indoors nor outdoors) . And kills the asura by laying him on His thighs (neither on earth nor in the sky)!
The Fifth Avatar - Vaamana (Brahmin boy)
Object of Incarnation - To prevent the righteous King Mahabali (King of Asuras) from taking over the heavens. He was performing the Viswajit sacrifice with that aim, guided by Sukracharya. The small brahmin goes to Bali and demands a strip of land three paces long, measure by his own feet. As soon as Mahabali gives his consent the boy starts growing till his first stride measure the whole of the earth, and the second the Heavens. And being a man of his word, Bali asks Vishnu to measure his third stride on his head, which he does and pushes Bali to the nether-worlds. Vishnu is so pleased by the Asura's righteousness, that he lets Mahabali come to earth every once a year to visit his people. (Aithihya says that his annual visit is the festival celebrated as ONAM by the malayalees)
The Sixth Avatar - Parasurama (the Ascetic warrior)
Object of Incarnation - To destroy all the evil Kshatriyas like Arjuna of the Haihayas. Vishnu was born as Rama son of the ascetic Jamadagni and his wife Renuka. Though the son of a sage he was an expert with weapons, his favourite being the Axe (Parashu). King Arjuna steals Kamadhenu from Rama's ashram in his absence and he kills Arjuna. But in turn Arjuna's son wrecks havock and kills Jamadagni. In his rage , Parashurama vows to wipe out the ksatriyas 21 times (the same number his mother beat her breast and lamented). King Dasharatha (father of the next avatar Rama) hides in the ladies' quarters in disguise and thus escapes.
The Seventh Avatar - Rama (the Kshatriya)
Described in the Epic called 'Ramaayana'
Object of Incarnation - To put an end to the asura king Ravana and his atrocities. It is said that an amsha (part)of Vishnu was manifest in all the four sons of Dasharatha. But it is also said that his favourite brother Lakshmana was the incarnation of the serpent Ananda (on whom Lord Vishnu lay). Sita is said to be the incarnation of Goddess Lakshmi. Also there is a part in Ramayana where Parashurama (The sixth)and Rama confront each other.
The Eighth Avatar - Krishna (the Yadava)
Described in the Epic called 'Mahabharata' of which Bhagavad Gita is a great part.
Object of Incarnation - To wipe out evil kings like Kamsa, Shishupala, Jarasandha and the whole Yadava race. The most powerful of all the incarnations.Born as the eight son of King Vasudeva and Devaki. Also his Gitopadesha to Arjuna during the Kurukshethra war (Bhagavad Gita) helps people understand the purpose of being and how to make the journey, whose ultimate goal is One-ness with Him.
The Ninth Avatar - Buddha (the Enlightened one)
Object of Incarnation - To spread peace and enligtenment among the folk, who lost their way to the Supreme. Prince Siddhartha of Kapilavastu, was born in the Lumbini Gardens under a Sal tree. He was upset by the truth of illnesses, old age and death that had been kept from him by his parents. Siddhartha was greatly influence when he saw a peaceful and calm ascetic between all the sufferings of the others. He renounced his life at the palace and started his quest for truth. He found it under a Bodhi tree and hence came to be known as Bodhisatva or Buddha. His first sermon was held at the Deer park at Sarnath near Varanasi. His teachings influenced so many people and filled them with such calm and peace that a separate religion known as Buddhism was founded on his teachings.
This essentially makes a person dwell upon the truth that no matter what path we take, the final goal is to be One with Him.
The Tenth Avatar - Kalki (the Exterminator)
Object of Incarnation - To wipe out the robbers, murderers and corrupt forces by the millions when the Kali yuga reaches it's nadir.To reinforce the Moral sense and humanitarian views in the good people.
