SB 10.3.31

viśvaṁ yad etat sva-tanau niśānte
 yathāvakāśaṁ puruṣaḥ paro bhavān
bibharti so ’yaṁ mama garbhago ’bhūd
 aho nṛ-lokasya viḍambanaṁ hi tat
Synonyms: 
viśvam — the entire cosmic manifestation; yat etat — containing all moving and nonmoving creations; sva-tanau — within Your body; niśā-ante — at the time of devastation; yathā-avakāśam — shelter in Your body without difficulty; puruṣaḥ — the Supreme Personality of Godhead; paraḥ — transcendental; bhavān — Your Lordship; bibharti — keep; saḥ — that (Supreme Personality of Godhead); ayam — this form; mama — my; garbha-gaḥ — came within my womb; abhūt — it so happened; aho — alas; nṛ-lokasya — within this material world of living entities; viḍambanam — it is impossible to think of; hi — indeed; tat — that (kind of conception).
Translation: 
At the time of devastation, the entire cosmos, containing all created moving and nonmoving entities, enters Your transcendental body and is held there without difficulty. But now this transcendental form has taken birth from my womb. People will not be able to believe this, and I shall become an object of ridicule.
Purport: 

As explained in Caitanya-caritāmṛta, loving service to the Personality of Godhead is of two different kinds: aiśvarya-pūrṇa, full of opulence, and aiśvarya-śīthila, without opulence. Real love of Godhead begins with aiśvarya-śīthila, simply on the basis of pure love.

premāñjana-cchurita-bhakti-vilocanena
 santaḥ sadaiva hṛdayeṣu vilokayanti
yaṁ śyāmasundaram acintya-guṇa-svarūpaṁ
 govindam ādi-puruṣaṁ tam ahaṁ bhajāmi

(Brahma-saṁhitā 5.38)

Pure devotees, whose eyes are anointed with the ointment of prema, love, want to see the Supreme Personality of Godhead as Śyāmasundara, Muralīdhara, with a flute swaying in His two hands. This is the form available to the inhabitants of Vṛndāvana, who are all in love with the Supreme Personality of Godhead as Śyāmasundara, not as Lord Viṣṇu, Nārāyaṇa, who is worshiped in Vaikuṇṭha, where the devotees admire His opulence. Although Devakī is not on the Vṛndāvana platform, she is near the Vṛndāvana platform. On the Vṛndāvana platform the mother of Kṛṣṇa is mother Yaśodā, and on the Mathurā and Dvārakā platform the mother of Kṛṣṇa is Devakī. In Mathurā and Dvārakā the love for the Lord is mixed with appreciation of His opulence, but in Vṛndāvana the opulence of the Supreme Personality of Godhead is not exhibited.

There are five stages of loving service to the Supreme Personality of Godhead — śānta, dāsya, sakhya, vātsalya and mādhurya. Devakī is on the platform of vātsalya. She wanted to deal with her eternal son, Kṛṣṇa, in that stage of love, and therefore she wanted the Supreme Personality of Godhead to withdraw His opulent form of Viṣṇu. Śrīla Viśvanātha Cakravartī Ṭhākura illuminates this fact very clearly in his explanation of this verse.

Bhakti, bhagavān and bhakta do not belong to the material world. This is confirmed in Bhagavad-gītā (14.26):

māṁ ca yo ’vyabhicāreṇa
 bhakti-yogena sevate
sa guṇān samatītyaitān
 brahma-bhūyāya kalpate

“One who engages in the spiritual activities of unalloyed devotional service immediately transcends the modes of material nature and is elevated to the spiritual platform.” From the very beginning of one’s transactions in bhakti, one is situated on the transcendental platform. Vasudeva and Devakī, therefore, being situated in a completely pure devotional state, are beyond this material world and are not subject to material fear. In the transcendental world, however, because of pure devotion, there is a similar conception of fear, which is due to intense love.

As stated in Bhagavad-gītā (bhaktyā mām abhijānāti yāvān yaś cāsmi tattvataḥ) and as confirmed in Śrīmad-Bhāgavatam (bhaktyāham ekayā grāhyaḥ), without bhakti one cannot understand the spiritual situation of the Lord. Bhakti may be considered in three stages, called guṇī-bhūta, pradhānī-bhūta and kevala, and according to these stages there are three divisions, which are called jñāna, jñānamayī and rati, or premā — that is, simple knowledge, love mixed with knowledge, and pure love. By simple knowledge, one can perceive transcendental bliss without variety. This perception is called māna-bhūti. When one comes to the stage of jñānamayī, one realizes the transcendental opulences of the Personality of Godhead. But when one reaches pure love, one realizes the transcendental form of the Lord as Lord Kṛṣṇa or Lord Rāma. This is what is wanted. Especially in the mādhurya-rasa, one becomes attached to the Personality of Godhead (śrī-vigraha-niṣṭha-rūpādi). Then loving transactions between the Lord and the devotee begin.

The special significance of Kṛṣṇa’s bearing a flute in His hands in Vrajabhūmi, Vṛndāvana, is described as mādhurī … virājate. The form of the Lord with a flute in His hands is most attractive, and the one who is most sublimely attracted is Śrīmatī Rādhārāṇī, Rādhikā. She enjoys supremely blissful association with Kṛṣṇa. Sometimes people cannot understand why Rādhikā’s name is not mentioned in Śrīmad-Bhāgavatam. Actually, however, Rādhikā can be understood from the word ārādhana, which indicates that She enjoys the highest loving affairs with Kṛṣṇa.

Not wanting to be ridiculed for having given birth to Viṣṇu, Devakī wanted Kṛṣṇa, with two hands, and therefore she requested the Lord to change His form.