In the Bhagwad Gita Lord Krishna says~
यदा यदा हि धर्मस्यग्लानिर्भवति भारत: ।
अभ्युत्थानमधर्मस्य तदात्मानं सृजाम्यहम् ॥
yada yada hi dharmasya glanir bhavati bharata
abhyutthanam adharmasya tadatmanam srjamy aham
(To translate…whenever and wherever there is a decline in the practice of ‘dharma’, O descendant of Bharata, and there is a predominance of ‘adharma’, at that time i will manifest myself)
It is one of the core beliefs contained in our scriptures…the conviction that Lord Vishnu the preserver of the Universe will incarnate from time to time to uproot injustice and eradicate the evil forces that threaten the existence of mankind and restore cosmic order. He is believed to have taken on nine incarnations or avatars till now and the tenth avatar is supposed to descend upon earth at the end of Kali Yuga. Collectively these ten incarnations are referred to as the ‘Dashavatar’. Many a study has sought to interpret this to be reflective of the idea of evolution from simple life forms to more complex ones. Others see in this story the foreshadowing of the modern Darwinian Theory of Evolution, a rough idea of the ‘vertebrate-evolution’ from a fish, a tortoise, a boar, a man-lion, a dwarf followed by four species of men.
In terms of the Vedic time-cycle the first four avatars descended on Earth during the Sat Yuga; the next three in Treta Yuga; the eighth and ninth in Dwapar Yuga; the tenth, it is believed will take birth at the end of the present Kali Yuga.
A brief look at these ten incarnations of Vishnu and the stories associated with them (a note here, do remember this is the standard list which may vary from region to region and even sect to sect!) As for figuring out the symbolism and historical significance of these stories…that is best left to scholars and their research studies!
# Matsya: At the beginning of Sat Yuga, during the Great Flood, Lord Vishnu took the form of Matsya—the fish—and rescued Manu and other beings who were in the boat. (Incidentally, this is not the Biblical story of Noah and his ark!!). Manu was the first human on earth and the progenitor of the human race. During the Great Flood, he took one specimen of each species in his boat and Lord Vishnu in his Matsya avatar helped him take his boat to the new world.
# Kurma: The next avatar of Vishnu appeared during the famous churning of the cosmic ocean during the Sat Yuga. Mount Mandrachala was being used as the churning staff, but the ocean was too deep and Mandrachala began to drown. The Lord then took the form of a giant tortoise and bore the weight of the mountain on his back.
# Varaha: In Sanskrit the word ‘varaha’ translates to a wild-boar. The story goes that a demon named Hiranyaksha carried the earth to the bottom of the cosmic ocean. Lord Vishnu took the form of a wild boar to free ‘prithvi’ or the earth. Their battle lasted for a thousand years and the demon was finally killed. Varaha then carried the earth out of the ocean between his tusks and restored it to its original place in the universe.
# Narasimha: This is a ferocious incarnation of Vishnu in the form of a half-lion and half-human from the Sat Yuga. The Lord appeared in this form to kill a demon named Hiranyakashipu (the elder brother of Hiranyaksha). He had wanted to avenge his brother and through penance had received a boon that he could be killed neither by man nor animal, neither inside the house nor outside, not at day nor at night, not on earth nor in the sky and not with any weapon. So Lord Vishnu in the anthropomorphic form of half-human half-lion, killed the demon with his claws at dusk, at the threshold of his house taking the demon on his thighs.
# Vamana: Lord Vishnu appeared in this Avatar in the Treta Yuga. It was a time when the immensely powerful demon king Bali (the fourth descendant of Hiranyakashipu) had taken control of the three worlds forcefully from the Gods. Bali was known to be extremely proud of his benevolence and charity. So when the Gods appealed to Vishnu, he took the form of a Vamana or Brahmin-dwarf and asked him for three paces of land which Bali agreed to grant. The dwarf then changed his size and became a giant. In two steps the Lord covered heaven and the underworld. Bali immediately realised the dwarf was none other than Vishnu and in deference offered him his head to step over. The story says as the Lord stepped over Bali’s head, Bali went inside the earth. Vishnu granted him immortality and made him the ruler of ‘patala’ or the nether-world.
# Parshuram: He was the first Brahmin-Kshatriya in the scriptures and was born to put an end to the tyrannical rule of the kshatriyas in Treta Yuga. Through his worship of Lord Shiva he acquired a divine axe which then helped him wipe out the tyrannical race. As per one account, he is an immortal (chiranjiv) who is still alive, doing penance for his killings.
# Ram, the prince of Ayodhya who vanquished the demon king Ravana in the Treta Yuga. He is considered to be the ‘ideal’ man. The tale of this protagonist of the epic Ramayana is known the world over.
# Krishna, like Ram is probably the most popular and revered incarnations of Lord Vishnu. In the Dwapar Yuga, he was born to kill his evil maternal uncle Kamsa; but is known more as the central character of the epic Mahabharata and for his sermon to Arjuna that forms the Bhagwad Gita.
# Buddha (or Balaram): There is some controversy regarding the ninth avatar with some regarding Gautam Buddha as the ninth avatar and others claiming it was Balaram, the elder brother of Krishna.
# Kalki: Kalki or the destroyer of evil it is said will take birth at the end of the present Kali Yuga. The scriptures talk of the Lord appearing riding a white horse, carrying a blazing sword in his hand and destroying all evil. It is also said that the Kalki avatar will initiate the next cycle, a new Sat Yuga by preserving righteousness.