The Supreme One has five forms — para, vyuha, antaryami, vibhava and archa. As antaryami, He is resident in every one of us. Vedanta Desika, in his Varadaraja Panchasat, marvels at Lord Narayana’s compassion towards us, said M.A. Venkatakrishnan in a discourse.
His abode is Sri Vaikuntha, the place where there is nothing but joy. And yet He chose to stay inside the cramped space of every person’s heart (sushiram susukshmam). And this heart is in a body, which is antahkalebaram — impure. And yet He chose to dwell inside such a body, which is entirely due to His mercy, says Desika. Paramapada is His abode, and the name itself implies that there is no other place superior to it, and yet He who should be there, is glad to be inside our hearts. And yet, the Lord is not content with this alone. He takes avataras, to save us. He gave us the Sastras, to show us the right path. But since we paid no heed to any of His instructions, but continued to do as we pleased, He assumed vibhava avataras, for our sake. As Rama and Krishna, He lived in our midst, to show us the right path. Had He not come down, we would have said it was easy for Him to lay down rules, but they were too difficult to be followed. So He came down and lived on this earth.
When a child falls ill, mother takes a medicine, so that its healing effect will reach the child through her milk. The Lord, likewise swallowed a medicine for our sake. That is, He adhered to the same Sastras, while He lived on this earth, to show that it was possible for a human being to keep to the right path. Avatara means He descended, for He was indeed coming from a higher plane, when He came to this earth. Pillai Lokacharya says that the earth was the place He jumped into, to save us.