The words bṛhate namas te have been explained by Śrīla Viśvanātha Cakravartī Ṭhākura: bṛhate śrī-kṛṣṇāya. The Supreme Personality of Godhead is Kṛṣṇa. There are many tattvas, such as viṣṇu-tattva, jīva-tattva and śakti-tattva, but above everything is the viṣṇu-tattva, which is all-pervading. This all-pervading feature of the Supreme Personality of Godhead is explained in Bhagavad-gītā (10.42), wherein the Lord says:

athavā bahunaitena
 kiṁ jñātena tavārjuna
viṣṭabhyāham idaṁ kṛtsnam
 ekāṁśena sthito jagat

“But what need is there, Arjuna, for all this detailed knowledge? With a single fragment of Myself I pervade and support this entire universe.” Thus Kṛṣṇa says that the entire material world is maintained by His partial representation as Paramātmā. The Lord enters every universe as Garbhodakaśāyī Viṣṇu and then expands Himself as Kṣīrodakaśāyī Viṣṇu to enter the hearts of all living entities and even enter the atoms. Aṇḍāntara-stha-paramāṇu-cayāntara-stham. Every universe is full of atoms, and the Lord is not only within the universe but also within the atoms. Thus within every atom the Supreme Lord exists in His Viṣṇu feature as Paramātmā, but all the viṣṇu-tattvas emanate from Kṛṣṇa. As confirmed in Bhagavad-gītā (10.2), aham ādir hi devānām: Kṛṣṇa is the ādi, or beginning, of the devas of this material world — Brahmā, Viṣṇu and Maheśvara. Therefore He is described here as bhagavate bṛhate. Everyone is bhagavān — everyone possesses opulence — but Kṛṣṇa is bṛhān bhagavān, the possessor of unlimited opulence. Īśvaraḥ paramaḥ kṛṣṇaḥ. Kṛṣṇa is the origin of everyone. Ahaṁ sarvasya prabhavaḥ. Even Brahmā, Viṣṇu and Maheśvara come from Kṛṣṇa. Mattaḥ parataraṁ nānyat kiñcid asti dhanañjaya: there is no personality superior to Kṛṣṇa. Therefore Viśvanātha Cakravartī Ṭhākura says that bhagavate bṛhate means “unto Śrī Kṛṣṇa.”

In this material world, everyone is a paśu, an animal, because of the bodily conception of life.

yasyātma-buddhiḥ kuṇape tri-dhātuke
 sva-dhīḥ kalatrādiṣu bhauma ijya-dhīḥ
yat tīrtha-buddhiḥ salile na karhicij
 janeṣv abhijñeṣu sa eva go-kharaḥ

“A human being who identifies the body made of three elements as the self, who considers the by-products of the body to be his kinsmen, who considers the land of his birth to be worshipable, and who goes to a place of pilgrimage simply to bathe rather than to meet men of transcendental knowledge there is to be considered like a cow or an ass.” (Bhāg. 10.84.13) Practically everyone, therefore, is a paśu, an animal, and everyone is attacked by the crocodile of material existence. Not only the King of the elephants but every one of us is being attacked by the crocodile and is suffering the consequences.

Only Kṛṣṇa can deliver us from this material existence. Indeed, He is always trying to deliver us. Īśvaraḥ sarva-bhūtānāṁ hṛd-deśe ’rjuna tiṣṭhati. He is within our hearts and is not at all inattentive. His only aim is to deliver us from material life. It is not that He becomes attentive to us only when we offer prayers to Him. Even before we offer our prayers, He incessantly tries to deliver us. He is never lazy in regard to our deliverance. Therefore this verse says, bhūri-karuṇāya namo ’layāya. It is the causeless mercy of the Supreme Lord that He always tries to bring us back home, back to Godhead. God is liberated, and He tries to make us liberated, but although He is constantly trying, we refuse to accept His instructions (sarva-dharmān parityajya mām ekaṁ śaraṇaṁ vraja). Nonetheless, He has not become angry. Therefore He is described here as bhūri-karuṇāya, unlimitedly merciful in delivering us from this miserable material condition of life and taking us back home, back to Godhead.