The complete expression of Sanskrit is AVATARYETI , it means steped down from up. Not incarnation of God.
In Bhartiya mythology following 24 AVATARS came to earth in Bharat:
Lord Vishnu took his first incarnation as the pre-eminent man, with a desire to commence creation. This first incarnation of Lord Vishnu was full of all the sixteen Kalas (Supernatural powers; phases).
Lord Brahma manifested, from the navel of Lord Vishnu in his (Lord Vishnu) state of Yoganidra (deep meditation). The creation as well as the expansion of the creation commenced from the organs of Lord Brahma. The first incarnation of Lord Vishnu is all-powerful, which can be seen only by the yogies (sages) who have attained divine knowledge and status. This incarnation is also the indestructible seed from which all the other incarnations manifest themselves. During the time of final annihilation of the world, every creation merges into him.
2. THE ETERNAL YOUTHS :
Sanatkumar was the 'Manasputra' (born by a wish) of Lord Brahma. Throughout his life, he maintained celibacy (no sex, bramhacharya); and engaged himself in the performance of tremendous penance (deep meditation). He was the one from whom the Brahmins got the inspiration regarding the values and importance of penance and Celibacy.
3. VARAHA AVATAR (The incarnation as a Boar) :
Lord Vishnu took his third incarnation as a boar. In this incarnation Lord Vishnu rescued the earth which had submerged in the ocean, and brought it out from the ocean. The whole creation started only after that. A demon by the name of Hiranyaksha had abducted the earth and carried it to the 'Rasatala' (the second lowest of the world). The earth is considered to be as a 'Woman' and since it is a crime to abduct a woman therefore Lord Vishnu in his incarnation of a boar killed the demon Hiranyaksha and liberated the whole creation started only after that. Whole creation started only after that.
May be he corrected the trajectory of earth.
4. NARADA AVATAR (The incarnation as Sage Narada) :
Lord Vishnu took his fourth incarnation as Narada. Narada by becoming a “Devarishi” among all sages. He achieved liberation, from all of his Karma's (deeds). Narada was the one who gave discourses to the Vaishnavas (followers of Lord Vishnu) on 'Pancharatra Tantra'.
Lord Vishnu in his incarnation as Narada, showed that, the devotion (worshiping) is the best mean of getting liberated from all the bondages of 'Karma's'. He also said that a devotee of Lord Vishnu is the supreme among the devotees in the same way as Devarishi Narada among the Sages.
5. NARA-NARAYANA AVATAR (Incarnation as Nara-Narayana) :
Lord Vishnu took his fifth incarnation as sage Nara-Narayan by taking a birth from the womb of a woman named 'Kala'. He performed a tremendous penance by going to places, Badri nath and Kedar nath. He showed the importance Penance, and also that nothing can be achieved in this world without it.
6. KAPILA AVATAR (Incarnation as Sage Kapila) :
Lord Vishnu's Sixth incarnation was as sage Kapila. The objective of this incarnation was to compile all the divine knowledge that had been destroyed. He was the profounder of Sankhya Yoga (rationalism) which helped the Brahmins, who had forgotten their duties to rectify their mistakes. He also gave discourse to his own mother.
7. DATTATRAYA AVATAR (Incarnation as Dattatraya) :
Lord Vishnu's Seventh incarnation was as Dattatraya. He was born to Ansuya and his father was Sage Atri. He was the one who had given Spiritual Knowledge to King Alarka and Prahlada. He had twenty four teachers. He believed that in the world, a man can learn from each and every thing, so he accepted twenty-four objects like water, bird, air, an unmarried girl, even a prostitute, etc.
8. YAGYA AVATAR (Incarnation as Yagya):
Lord Vishnu in his eighth incarnation as Yagya was born to Prajapati and Akuti.
He had rescued a 'Devagana' (celestial and supernatural being) named Yama and also the Manvantar named as 'Swayambhuva'. The main thrust of his teaching was based on the values of helpfulness and protecting each other during the time of crisis.
Lord Vishnu in his ninth incarnation as Rishabh Dev was born to king Nabhi
and Marudevi. His mother Marudevi was the daughter of Indra. He attained that state of Param-hansa (an ascetic of highest order who has controlled his anger) which is an uphill task. He was given the title of 'Jin' which meansa ' a knower'. His followers are known as Jains.
Lord Vishnu in his tenth incarnation as 'Prithu' came into existence after the body of King 'Vena'. Lord Vishnu took this incarnation as per the wishes of the sages. The earth had concealed all the vegetation's within her and as a result the whole land had become barren. To protect the humanity, Lord Vishnu took incarnation as Prithu by milking the cow (earth). This is considered that as a very supreme incarnation, because the earth has remained full of vegetation's after that.
11. MATSYA AVATAR (Incarnation as a Fish) :
All the oceans had unified into a single ocean in the 'Manvantara' of 'Chakshusha'. Lord Vishnu in his 11th incarnation as a Matsya (Fish) rescued the earth from 'Maya' the demon. He gave discourses to Satyavrat along with the seven sages, while they were sitting on the boat. He also showed them his illusionary powers. This was his eleventh incarnation.
May be he corrected the trajectory of earth.
12. KACHCHAP AVATAR (Incarnation as a Tortoise) :
Lord Vishnu in his twelfth incarnation as a tortoise, held the mountain 'Mandarachala' on his back, during the time when the deities and the demons where churning the ocean. He stopped the mountain from going to the netherworld. This was Lord Vishnu's twelfth incarnation.
May be he corrected the trajectory of earth.
13. DHANVANTARI (Incarnation as Dhanvantari) :
Lord Vishnu took his thirteenth incarnation as Dhanvantari. He manifested from the ocean holding a vessel filled with ambrosia. He was the profounder of medicinal science.
14. MOHINI AVATAR (Incarnation as a most Enchanting woman) :
Lord Vishnu in his fourteenth incarnation as a most enchanting woman enchanted the demons by his beautiful appearance of a woman, and took away the pot filled up with ambrosia from them and gave it to the deities. The deities were thus protected from the demons.
15. NARSIMHA AVATAR (Incarnation in the form of half-man & half-lion) :
Lord Vishnu took his fifteenth incarnation as Narisimha, having upper portion of his body in the form of lion and the lower portion resembling of a man. In this incarnation he protected Prahlada from his father Hiranyakashipu the demon. He killed Hiranyakashipu by tearing his body apart by his nails. Lord Vishnu had to attain this form because Lord Brahma had blessed Hiranyakashipu, that a Human being could not kill him.
16. HAYAGREEVA AVATAR (Incarnation as Hayagreeva) :
Once Lord Brahma becoming tired of his creative activities, wanted to rest. The night of the Brahma was approaching. Because of his tiredness Lord Brahma yawned. All the four Vedas came out from his opened mouth. A demon who used to live near him in disguise, abducted the Vedas. Lord Vishnu took his sixteenth incarnation as Hayagreeva to protect the Vedas. In this incarnation his face resembled that of a horse and the rest of his body resembled that of Sri Narayan with all of his four hands. He killed the demon and protected the Vedas.
17. VAMAN AVATAR (Incarnation as a Dwarf) :
Lord Vishnu took his seventeenth incarnation as a Dwarf, when Bali the king of the demons had captured the entire three worlds. Indra and all the other deities were wandering all around after losing the heaven.
To help the deities regain control over the heaven. Lord Vishnu disguised as a dwarf went to Bali, when he was busy performing a 'Yagya' and demanded earth measured by his three steps. When 'Bali' agreed, he transformed his form from a small dwarf to a giant. Consequently he covered the entire three worlds with his two steps. Ultimately he regained heaven for the deities.
(There is a side storey; The residence of the looser is never confiscated. So King Bali was left with his huge palace only, with 36 doors.
At the end of above episode, Vaman asked what you want as blessing. King Bali desired; whenever I come out my place, I should see you first. In turn Lord Vishnu had to keep on making rounds around his place (palace), as King Bali may come out any time from any door.)
18. PARSHURAM AVATAR (Incarnation as Parshurama) :
When the Kshatriya kings became ruthless and started exploiting their subjects. Lord Vishnu took his eighteenth incarnation as Parshurama' and annihilated the Kshatriyas kings for seventeen times and consequently donated the earth to the Brahmins.
19. VYAS AVATAR (Incarnation as Sage Vyas) :
Lord Vishnu took his nineteenth incarnation as Sage Vyasa by taking birth from the womb of 'Satyavati'. His father was sage Parashar. He made the division of Veda, and made extension of its branches.
· He also wrote eighteen Maha-puranas. Mahabharata as well as Shri Mad Bhagwat was written by him. GEETA the most respected book for a Sanatani, containing knowledge of all mythological scriptures is also part of Mahabharata.
· One might have not noticed, Kaurava as well Pandavea were his decedents only.
20. RAM AVATAR (Incarnation as Lord Rama) :
Lord Rama is considered to be the twentieth incarnation of Lord Vishnu. In this incarnation he constructed a bridge over the ocean with the help of the Vanars (monkeys) and after crossing over to Lankas killed many demons like Ravana, Kumbhakarna. He accomplished many astonishing feats and saved the deities. He taught the value of morality.
Balrama is considered to be the twenty-first incarnation of Lord Vishnu. In this incarnation he killed Pralambasura the demon and he killed many more demons.
22. KRISHNA AVATAR (Incarnation as Krishna) :
Lord Krishna born in Mathura was the twenty-second incarnation of Lord Vishnu. He fought against the exploitation right from his childhood and killed many demons like Kalayavan, Kansa, Jarasandh etc. He gave a divine knowledge to Arjun during the battle of Kurukshetra.
23. BUDDHA AVATAR (Incarnation as Buddha) :
The twenty-third incarnation of Lord Vishnu was as Lord Buddha. In the Kaliyuga the demons were completely subjugated by the deities. Shukracharya the teacher of the demons instigated the demons to perform Yagya so that they could regain power and authority. Fearing this, the deities prayed to Lord Vishnu for help. Lord Vishnu took incarnation as Buddha and dissuaded the demons from performing Yagya as it involves violence the demons
24. KALKI AVATAR (Incarnation as Kalki) :
At the end of Kaliyuga, when the sins would be at its maximum and all pervading that the kings would themselves becomes thieves. Then Lord Vishnu would take his twenty-fourth incarnation as Kalki by taking birth in the village of 'Shambhal'. He would take birth in a Brahmin family of Vishnuyash. By killing and destroying the sinners, he would re-establish the superiority of Virtuosity and religiousness.
At other place, they have considered 10 Avatars only.
1 Matsya (the fish)
2. Koorma (the tortoise)
3. Varaha (the boar)
4. Narasimha (the human-lion)
5.Vamana (the dwarf)
6. Parasurama (the angry man, Rama with an axe)
7. Lord Rama (the perfect man, king of Ayodha)
8. Lord Krishna (the divine statesman)
9. Balarama (elder brother of Krishna)
10. Kalki (the mighty worrior)
This means it is opinion of the script writer; not an authentic fact.
At the same time, none was perfect. Of course
· They were very intelligent,
· The preached new dimensions of spiritualism
· The executed the jobs very intelligently and bravely.
But if they were incarnations of God they had o be completely right and perfect as He himself.
There is another perspective. They were messengers, prophets or representative of God; but not himself. The literal meaning of Avatar is same.
They cannot be called son of God, as we all are.
We all are created by God, in turn we all his sons.