SB 1.3.5
etan nanavataranam
nidhanam bijam avyayam
yasyamsamsena srjyante
deva-tiryan-naradayah
Translation by His Divine Grace A. C. Bhaktivedanta Swami Srila Prabhupada:
This form [the second manifestation of the purusa] is the source and indestructible seed of multifarious incarnations within the universe. From the particles and portions of this form, different living entities, like demigods, men and others, are created.
Purport by His Divine Grace A. C. Bhaktivedanta Swami Srila Prabhupada:
The purusa, after creating innumerable universes in the mahat-tattva, entered in each of them as the second purusa, Garbhodakasayi Visnu. When He saw that within the universe there was only darkness and space, without a resting place, He filled half of the universe with water from His own perspiration and laid Himself down on the same water. This water is called Garbhodaka. Then from His navel the stem of the lotus flower sprouted, and on the flower petals the birth of Brahma, or the master engineer of the universal plan, took place. Brahma became the engineer of the universe, and the Lord Himself took charge of the maintenance of the universe as Visnu. Brahma was generated from rajo-guna of prakrti, or the mode of passion in nature, and Visnu became the Lord of the mode of goodness. Visnu, being transcendental to all the modes, is always aloof from materialistic affection. This has already been explained. From Brahma there is Rudra (Siva), who is in charge of the mode of ignorance or darkness. He destroys the whole creation by the will of the Lord. Therefore all three, namely Brahma, Visnu and Siva, are incarnations of the Garbhodakasayi Visnu. From Brahma the other demigods like Daksa, Marici, Manu and many others become incarnated to generate living entities within the universe. This Garbhodakasayi Visnu is glorified in the Vedas in the hymns of Garbha-stuti, which begin with the description of the Lord as having thousands of heads, etc. The Garbhodakasayi Visnu is the Lord of the universe, and although He appears to be lying within the universe, He is always transcendental. This also has already been explained. The Visnu who is the plenary portion of the Garbhodakasayi Visnu is the Supersoul of the universal life, and He is known as the maintainer of the universe or Ksirodakasayi Visnu. So the three features of the original purusa are thus understood. And all the incarnations within the universe are emanations from this Ksirodakasayi Visnu.
In different millennia there are different incarnations, and they are innumerable, although some of them are very prominent, such as Matsya, Kurma, Varaha, Rama, Nrsimha, Vamana and many others. These incarnations are called lila incarnations. Then there are qualitative incarnations such as Brahma, Visnu and Siva (or Rudra) who take charge of the different modes of material nature.
Lord Visnu is nondifferent from the Personality of Godhead. Lord Siva is in the marginal position between the Personality of Godhead and the living entities, or jivas. Brahma is always a jiva-tattva. The highest pious living being, or the greatest devotee of the Lord, is empowered with the potency of the Lord for creation, and he is called Brahma. His power is like the power of the sun reflected in valuable stones and jewels. When there is no such living being to take charge of the post of Brahma, the Lord Himself becomes a Brahma and takes charge of the post.
Lord Siva is not an ordinary living being. He is the plenary portion of the Lord, but because Lord Siva is in direct touch with material nature, he is not exactly in the same transcendental position as Lord Visnu. The difference is like that between milk and curd. Curd is nothing but milk, and yet it cannot be used in place of milk.
The next incarnations are the Manus. Within one day’s duration of the life of Brahma (which is calculated by our solar year as 4,300,000 × 1,000 years) there are fourteen Manus. Therefore there are 420 Manus in one month of Brahma and 5,040 Manus in one year of Brahma. Brahma lives for one hundred years of his age, and therefore there are 5,040 × 100 or 504,000 Manus in the duration of Brahma’s life. There are innumerable universes, with one Brahma in each of them, and all of them are created and annihilated during the breathing time of the purusa. Therefore one can simply imagine how many millions of Manus there are during one breath of the purusa.
The Manus who are prominent within this universe are as follows: Yajña as Svayambhuva Manu, Vibhu as Svarocisa Manu, Satyasena as Uttama Manu, Hari as Tamasa Manu, Vaikuntha as Raivata Manu, Ajita as Caksusa Manu, Vamana as Vaivasvata Manu (the present age is under the Vaivasvata Manu), Sarvabhauma as Savarni Manu, Rsabha as Daksa-savarni Manu, Visvaksena as Brahma-savarni Manu, Dharmasetu as Dharma-savarni Manu, Sudhama as Rudra-savarni Manu, Yogesvara as Deva-savarni Manu, and Brhadbhanu as Indra-savarni Manu. These are the names of one set of fourteen Manus covering 4,300,000,000 solar years as described above.
Then there are the yugavataras, or the incarnations of the millennia. The yugas are known as Satya-yuga, Treta-yuga, Dvapara-yuga and Kali-yuga. The incarnations of each yuga are of different color. The colors are white, red, black and yellow. In the Dvapara-yuga, Lord Krsna in black color appeared, and in the Kali-yuga Lord Caitanya in yellow color appeared.
So all the incarnations of the Lord are mentioned in the revealed scriptures. There is no scope for an imposter to become an incarnation, for an incarnation must be mentioned in the sastras. An incarnation does not declare Himself to be an incarnation of the Lord, but great sages agree by the symptoms mentioned in the revealed scriptures. The features of the incarnation and the particular type of mission which He has to execute are mentioned in the revealed scriptures.
Apart from the direct incarnations, there are innumerable empowered incarnations. They are also mentioned in the revealed scriptures. Such incarnations are directly as well as indirectly empowered. When they are directly empowered they are called incarnations, but when they are indirectly empowered they are called vibhutis. Directly empowered incarnations are the Kumaras, Narada, Prthu, Sesa, Ananta, etc. As far as vibhutis are concerned, they are very explicitly described in the Bhagavad-gita in the Vibhuti-yoga chapter. And for all these different types of incarnations, the fountainhead is the Garbhodakasayi Visnu.