1. Matsya Avatara - Incarnation as a Fish - (Translation of the holy verse) O Kesava!, in the form of Fish , In the waters of deluge, You held the Vedas like a vessel undeflected from its course. To preserve the knowledge of Vedas, You took the incarnation of Fish! Hail Hari, Lord of the universe!
Purport: The first avatara signifies the restoration of true knowledge (Vedas), recovered from the deluge of egoism, which has to be destroyed in the process.
2. Kurma Avathara - Incarnation as a Tortoise -
(Translation of the holy verse ) : O Kesava!, in the form of Tortoise (kacchaparupa), On the ample expanse of your back rests the world, creating circular marks. Hail Hari ! Lord of the universe!
Purport: The incarnation of God in the Tortoise form during the churning of the Ocean, signifies that the churning of the ocean of experience with the churn of knowledge, towards the Absolute can rest only on the immovable, all-sufficient, all-sustaining basis of self-evident truth, symbolized by the Tortoise avatara.
3. Varaha Avatara - Incarnation as a Boar
(Translation of the holy verse) : O Kesava!, in the form of the Boar (sukarupa)! The earth rests in peace on the tip of your tusk, like the marking on the disk of the moon. Hail Hari ! Lord of the universe!.
Purport: The Boar avatara is identified with sacrifice both in the Vishnupurana and Bhagavata. As sacrifice (of worldly affairs) is essential for the stability of mind for contemplation on God, it is symbolized by the Boar form of the Lord.
4. Narashima Avatara - Incarnation as a Half man, half beast (Translation of the holy verse) : O Kesava!, in the form of Man-Lion (naraharirupa)! The sharp nails on your hands became wonderful claws that tore up the body of demon Hiranyakasipu (To protect Prahlada). Hail Hari!