यस्यावतारा ज्ञायन्ते शरीरेष्वशरीरिणः तैस्तैरतुल्यातिशयैर्वीर्यैर्देहिष्वसंगतैः स भवान्सर्वलोकस्य भवाय विभवाय च अवतीर्णो ऽंशभागेन साम्प्रतं पतिराशिषाम्
yasyāvatārā jñāyante śarīreṣv aśarīriṇaḥ tais tair atulyātiśayair vīryair dehiṣv asaṅgataiḥ sa bhavān sarva-lokasya bhavāya vibhavāya ca avatīrṇo 'ṁśa-bhāgena sāmprataṁ patir āśiṣām
Synonyms
yasya—of whom; avatārāḥ—the different incarnations, like Matsya, Kūrma and Varāha; jñāyante—are speculated; śarīreṣu—in different bodies, differently visible; aśarīriṇaḥ—they are not ordinary material bodies, but are all transcendental; taiḥ taiḥ—by such bodily activities; atulya—incomparable; ati-śayaiḥ—unlimited; vīryaiḥ—by strength and power; dehiṣu—by those who actually have material bodies; asaṅgataiḥ—which activities, enacted in different incarnations, are impossible to be performed; saḥ—the same Supreme; bhavān—Your Lordship; sarva-lokasya—of everyone; bhavāya—for the elevation; vibhavāya—for the liberation; ca—and; avatīrṇaḥ—have now appeared; aṁśa-bhāgena—in full potency, with different parts and parcels; sāmpratam—at the present moment; patiḥ āśiṣām—You are the Supreme Personality of Godhead, the master of all auspiciousness..
Translation
Appearing in bodies like those of an ordinary fish, tortoise and hog, You exhibit activities impossible for such creatures to perform—extraordinary, incomparable, transcendental activities of unlimited power and strength. These bodies of Yours, therefore, are not made of material elements, but are incarnations of Your Supreme Personality. You are the same Supreme Personality of Godhead, who have now appeared, with full potency, for the benefit of all living entities within this material world.
Purport
As stated in Bhagavad-gītā (4.7-8):
yadā yadā hi dharmasya
glānir bhavati bhārata
abhyutthānam adharmasya
tadātmānaṁ sṛjāmy aham
paritrāṇāya sādhūnāṁ
vināśāya ca duṣkṛtām
dharma-saṁsthāpanārthāya
sambhavāmi yuge yuge
Kṛṣṇa appears as an incarnation when real spiritual life declines and when rogues and thieves increase to disturb the situation of the world. Unfortunate, less intelligent persons, bereft of devotional service, cannot understand the Lord's activities, and therefore such persons describe these activities as kalpanā—mythology or imagination—because they are rascals and the lowest of men (na māṁ duṣkṛtino mūḍhāḥ prapadyante narādhamāḥ). Such men cannot understand that the events described by Vyāsadeva in the purāṇas and other śāstras are not fictitious or imaginary, but factual.
Kṛṣṇa, in His full, unlimited potency, here shows that He is the Supreme Personality of Godhead, for although the two trees were so large and sturdy that even many elephants could not move them, Kṛṣṇa, as a child, exhibited such extraordinary strength that they fell down with a great sound. From the very beginning, by killing Pūtanā, Śakaṭāsura and Tṛṇāvartāsura, by causing the trees to fall, and by showing the entire universe within His mouth, Kṛṣṇa proved that He is the Supreme Personality of Godhead. The lowest of men (mūḍhas), because of sinful activities, cannot understand this, but devotees can accept it without a doubt. Thus the position of a devotee is different from that of a nondevotee.