The puruṣa, after creating innumerable universes in the mahat-tattva, entered in each of them as the second puruṣa, Garbhodakaśāyī Viṣṇu. 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 Brahmā, or the master engineer of the universal plan, took place. Brahmā became the engineer of the universe, and the Lord Himself took charge of the maintenance of the universe as Viṣṇu. Brahmā was generated from rajo-guṇa of prakṛti, or the mode of passion in nature, and Viṣṇu became the Lord of the mode of goodness. Viṣṇu, being transcendental to all the modes, is always aloof from materialistic affection. This has already been explained. From Brahmā there is Rudra (Śiva), 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 Brahmā, Viṣṇu and Śiva, are incarnations of the Garbhodakaśāyī Viṣṇu. From Brahmā the other demigods like Dakṣa, Marīci, Manu and many others become incarnated to generate living entities within the universe. This Garbhodakaśāyī Viṣṇu 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 Garbhodakaśāyī Viṣṇu 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 Viṣṇu who is the plenary portion of the Garbhodakaśāyī Viṣṇu is the Supersoul of the universal life, and He is known as the maintainer of the universe or Kṣīrodakaśāyī Viṣṇu. So the three features of the original puruṣa are thus understood. And all the incarnations within the universe are emanations from this Kṣīrodakaśāyī Viṣṇu.
In different millennia there are different incarnations, and they are innumerable, although some of them are very prominent, such as Matsya, Kūrma, Varāha, Rāma, Nṛsiṁha, Vāmana and many others. These incarnations are called līlā incarnations. Then there are qualitative incarnations such as Brahmā, Viṣṇu, and Śiva (or Rudra) who take charge of the different modes of material nature.
Lord Viṣṇu is nondifferent from the Personality of Godhead. Lord Śiva is in the marginal position between the Personality of Godhead and the living entities, or jīvas. Brahmā is always a jīva-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 Brahmā. 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 Brahmā, the Lord Himself becomes a Brahmā and takes charge of the post.