Translation by His Divine Grace A. C. Bhaktivedanta Swami Srila Prabhupada:
Dear Lord, we offer our respectful obeisances unto You because Your existence is completely independent of all material influences. Your Lordship always takes away the devotee’s miserable conditions, for Your brain plans how to do so. You live everywhere as Paramatma; therefore You are known as Vasudeva. You also accept Vasudeva as Your father, and You are celebrated by the name Krsna. You are so kind that You always increase the influence of all kinds of devotees.
Purport by His Divine Grace A. C. Bhaktivedanta Swami Srila Prabhupada:
In the previous verse it has been said (grhita-maya-guna-vigrahaya) that the Lord accepts three kinds of bodies (Visnu, Brahma and Siva) for the purposes of creating, maintaining and annihilating the cosmic manifestation. The three predominating deities of the material universe — Brahma, Visnu and Siva — are called guna-avataras. There are many kinds of incarnations of the Supreme Personality of Godhead, and the first incarnations within this material world are Brahma, Visnu and Mahesvara (Siva). Out of these three, Lord Brahma and Lord Siva accept material bodies, but Lord Visnu does not accept a material body. Lord Visnu is therefore known as visuddha-sattva. His existence is completely free from the contamination of the material modes of nature. One should therefore not think that Lord Visnu is in the same category with Lord Brahma and Siva. The sastras forbid us to think in this way:
yas tu narayanam devam
sa pasandi bhaved dhruvam
One who considers Lord Visnu to be in the same category with devas like Lord Brahma or Lord Siva or who thinks Lord Brahma and Siva to be equal to Lord Visnu is to be considered as pasandi, a faithless nonbeliever. Therefore in this verse Lord Visnu is distinguished in the words namo visuddha-sattvaya. Although a living entity like us, Lord Brahma is exalted due to his pious activities; therefore he is given the high post of Brahma. Lord Siva is not actually like a living entity, but he is not the Supreme Personality of Godhead. His position is somewhere between Visnu, the Supreme Personality of Godhead, and Brahma, the living entity. Lord Siva is therefore explained in Brahma-samhita (5.45) in this way:
ksiram yatha dadhi vikara-visesa-yogat
sañjayate na hi tatah prthag asti hetoh
yah sambhutam api tatha samupaiti karyad
govindam adi-purusam tam aham bhajami
Lord Siva is considered to be like yogurt (dadhi). Yogurt is nothing but transformed milk; nonetheless, yogurt cannot be accepted as milk. Similarly, Lord Siva holds almost all the powers of Lord Visnu, and he is also above the qualities of the living entity, but he is not exactly like Visnu, just as yogurt, although transformed milk, is not exactly like milk.
The Supreme Personality of Godhead is also described herein as vasudevaya krsnaya. Krsna is the original Supreme Personality of Godhead, and all Visnu expansions are His plenary portions or portions of His plenary portions (known as svamsa and kala). The svamsa, or direct expansion, is also called amsa. All visnu-tattvas are svamsa, direct parts and parcels of the Supreme Personality of Godhead, Krsna. Krsna is known as Vasudeva because He appeared in this material world as the son of Vasudeva. Similarly, He is known as Devaki-nandana, Yasoda-nandana, Nanda-nandana and so on.
Again and again the Lord is very much interested in increasing the influence of His devotees. Therefore He is described herein as prabhave sarva-satvatam. The satvata community is a community of Vaisnavas, pure devotees of the Lord. The Supreme Personality of Godhead has unlimited powers, and He wants to see that His devotees are also entrusted with unlimited powers. Therefore a devotee of the Lord is always distinguished from all other living entities.
The word hari means “one who takes away all miserable conditions,” and hari-medhase means that the Lord is always planning ways to deliver the conditioned soul from the clutches of maya. The Lord is so kind that He personally incarnates to deliver the conditioned souls, and whenever He comes, He makes His plans:
vinasaya ca duskrtam
sambhavami yuge yuge
“To deliver the pious and to annihilate the miscreants, as well as to reestablish the principles of religion, I Myself appear millennium after millennium.” (Bg. 4.8)
Since the Lord delivers all conditioned souls from the clutches of maya, He is known as hari-medhas. In the list of incarnations, Krsna is described as the supreme and original Personality of Godhead:
ete camsa-kalah pumsah
krsnas tu bhagavan svayam
mrdayanti yuge yuge
Krsna, the original Personality of Godhead, appears in this material world when the demigods, who are devotees of the Lord, are disturbed by the demons.