SB 1.2 - The purpose of the Lord's incarnations
Assuming the roles of incarnations, He performs pastimes to reclaim those in the mode of goodness. The Lord incarnates in each and every planet and in each and every type of living society. Without changing His transcendental position, He appears to be differently manifested according to the particular time, circumstances and society. The purpose of the incarnation is to create the desire in the living being to go back to Godhead. The eternal happiness the living being hankers for is found only in the kingdom of God. And the Lord personally comes or sends His representatives to give information about the kingdom of God and reclaim the fallen souls. The purpose of Kṛṣṇa’s incarnation is to rejuvenate the devotional service of hearing, remembering, worshiping, and so on so that the conditioned souls might get liberation.
The Lord appears as many forms when He enters all the living beings. However, He is without limitation or material contamination in all His forms. He appears in many forms with His svarūpa in His eternal pastimes.
In text 31 it was said that after creating the material substance, Lord Vāsudeva expands Himself and enters into it. Then in the form of Lord Viṣṇu, the Lord expands into all things (text 32) and into the hearts of all living beings (text 33), and enters each universe to perform pastimes (text 34).