SB 10.3.7-8

mumucur munayo devāḥ
 sumanāṁsi mudānvitāḥ
mandaṁ mandaṁ jaladharā
 jagarjur anusāgaram
niśīthe tama-udbhūte
 jāyamāne janārdane
devakyāṁ deva-rūpiṇyāṁ
 viṣṇuḥ sarva-guhā-śayaḥ
āvirāsīd yathā prācyāṁ
 diśīndur iva puṣkalaḥ
Word for word: 
mumucuḥ — showered; munayaḥ — all the great sages and saintly persons; devāḥ — and the demigods; sumanāṁsi — very beautiful and fragrant flowers; mudā anvitāḥ — being joyous in their attitude; mandam mandam — very mildly; jala-dharāḥ — the clouds; jagarjuḥ — vibrated; anusāgaram — following the vibrations of the sea waves; niśīthe — late at night; tamaḥ-udbhūte — when it was densely dark; jāyamāne — on the appearance of; janārdane — the Supreme Personality of Godhead, Viṣṇu; devakyām — in the womb of Devakī; deva-rūpiṇyām — who was in the same category as the Supreme Personality of Godhead (ānanda-cinmaya-rasa-pratibhāvitābhiḥ); viṣṇuḥ — Lord Viṣṇu, the Supreme Lord; sarva-guhā-śayaḥ — who is situated in the core of everyone’s heart; āvirāsīt — appeared; yathā — as; prācyām diśi — in the east; induḥ iva — like the full moon; puṣkalaḥ — complete in every respect.
Translation: 
The demigods and great saintly persons showered flowers in a joyous mood, and clouds gathered in the sky and very mildly thundered, making sounds like those of the ocean’s waves. Then the Supreme Personality of Godhead, Viṣṇu, who is situated in the core of everyone’s heart, appeared from the heart of Devakī in the dense darkness of night, like the full moon rising on the eastern horizon, because Devakī was of the same category as Śrī Kṛṣṇa.
Purport: 

As stated in the Brahma-saṁhitā (5.37):

ānanda-cinmaya-rasa-pratibhāvitābhis
 tābhir ya eva nija-rūpatayā kalābhiḥ
goloka eva nivasaty akhilātma-bhūto
 govindam ādi-puruṣaṁ tam ahaṁ bhajāmi

This verse indicates that Kṛṣṇa and His entourage are of the same spiritual potency (ānanda-cinmaya-rasa). Kṛṣṇa’s father, His mother, His friends the cowherd boys, and the cows are all expansions of Kṛṣṇa, as will be explained in the brahma-vimohana-līlā. When Brahmā took away Kṛṣṇa’s associates to test the supremacy of Lord Kṛṣṇa, the Lord expanded Himself again in the forms of the many cowherd boys and calves, all of whom, as Brahmā saw, were viṣṇu-mūrtis. Devakī is also an expansion of Kṛṣṇa, and therefore this verse says, devakyāṁ deva-rūpiṇyāṁ viṣṇuḥ sarva-guhā-śayaḥ.

At the time for the Lord’s appearance, the great sages and the demigods, being pleased, began to shower flowers. At the seashore, there was the sound of mild waves, and above the sea there were clouds in the sky which began to thunder very pleasingly.

When things were adjusted like this, Lord Viṣṇu, who is residing within the heart of every living entity, appeared in the darkness of night as the Supreme Personality of Godhead before Devakī, who appeared as one of the demigoddesses. The appearance of Lord Viṣṇu at that time could be compared to the rising of the full moon in the sky on the eastern horizon. The objection may be raised that since Lord Kṛṣṇa appeared on the eighth day of the waning moon, there could be no rising of the full moon. In answer to this it may be said that Lord Kṛṣṇa appeared in the dynasty which is in the hierarchy of the moon; therefore, although the moon was incomplete on that night, because of the Lord’s appearance in the dynasty wherein the moon is himself the original person, the moon was in an overjoyous condition, so by the grace of Kṛṣṇa he could appear as a full moon. To welcome the Supreme Personality of Godhead, the waning moon became a full moon in jubilation.

Instead of deva-rūpiṇyām, some texts of Śrīmad-Bhāgavatam clearly say viṣṇu-rūpiṇyām. In either case, the meaning is that Devakī has the same spiritual form as the Lord. The Lord is sac-cid-ānanda-vigraha, and Devakī is also sac-cid-ānanda-vigraha. Therefore no one can find any fault in the way the Supreme Personality of Godhead, sac-cid-ānanda-vigraha, appeared from the womb of Devakī.

Those who are not in full knowledge that the appearance and disappearance of the Lord are transcendental (janma karma ca me divyam) are sometimes surprised that the Supreme Personality of Godhead can take birth like an ordinary child. Actually, however, the Lord’s birth is never ordinary. The Supreme Personality of Godhead is already situated within the core of everyone’s heart as antaryāmī, the Supersoul. Thus because He was present in full potency in Devakī’s heart, He was also able to appear outside her body.

One of the twelve great personalities is Bhīṣmadeva (svayambhūr nāradaḥ śambhuḥ kumāraḥ kapilo manuḥ prahlāda, janako bhīṣmaḥ). In Śrīmad-Bhāgavatam (1.9.42), Bhīṣma, a great authority to be followed by devotees, says that the Supreme Personality of Godhead is situated in the core of everyone’s heart, just as the sun may be on everyone’s head. Yet although the sun may be on the heads of millions and millions of people, this does not mean that the sun is variously situated. Similarly, because the Supreme Personality of Godhead has inconceivable potencies, He can be within everyone’s heart and yet not be situated variously. Ekatvam anupaśyataḥ (Īśopaniṣad 7). The Lord is one, but He can appear in everyone’s heart by His inconceivable potency. Thus although the Lord was within the heart of Devakī, He appeared as her child. According to the Viṣṇu Purāṇa, therefore, as quoted in the Vaiṣṇava-toṣaṇī, the Lord appeared like the sun (anugrahāsaya). The Brahma-saṁhitā (5.35) confirms that the Lord is situated even within the atom (aṇḍāntara-stha-paramāṇu-cayāntara-stham). He is situated in Mathurā, in Vaikuṇṭha and in the core of the heart. Therefore one should clearly understand that He did not live like an ordinary child in the heart or the womb of Devakī. Nor did He appear like an ordinary human child, although He seemed to do so in order to bewilder asuras like Kaṁsa. The asuras wrongly think that Kṛṣṇa took birth like an ordinary child and passed away from this world like an ordinary man. Such asuric conceptions are rejected by persons in knowledge of the Supreme Personality of Godhead. Ajo ’pi sann avyayātmā bhūtānām īśvaro ’pi san (Bg. 4.6). As stated in Bhagavad-gītā, the Lord is aja, unborn, and He is the supreme controller of everything. Nonetheless, He appeared as the child of Devakī. This verse describes the inconceivable potency of the Lord, who appeared like the full moon. Understanding the special significance of the appearance of the Supreme Godhead, one should never regard Him as having taken birth like an ordinary child.