TEACHINGS OF QUEEN KUNTI
Chapter 17:

Śrīmad Bhāgavatam 1.8.34
bhārāvatāraṇāyānye
bhuvo nāva ivodadhau
sīdantyā bhūri-bhāreṇa
jāto hy ātma-bhuvārthitaḥ

bhāra-avatāraṇāya — just to reduce the burden to the world; anye — others; bhuvaḥ — of the world; nāvaḥ — boat; iva — like; udadhau — on the sea; sīdantyāḥ — aggrieved; bhūri — extremely; bhāreṇa — by the burden; jātaḥ — You were born; hi — certainly; ātma-bhuvā — by Brahmā; arthitaḥ — being prayed for.

TRANSLATION

Others say that the world, being overburdened like a boat at sea, is much aggrieved, and that Brahmā, who is Your son, prayed for You, and so You have appeared to diminish the trouble.

JOURNAL:

Srila Prabhupada opens this chapter thus:

Kuntīdevī is describing the different statements of different persons about why Kṛṣṇa appears.

When there is a need, the chief personalities in the universe approach Brahmā, who approaches Viṣṇu to ask that He reduce whatever the burden is. Then Viṣṇu or Kṛṣṇa appears as an incarnation, as stated in Bhagavad-gītā (4.7): 

yadā yadā hi dharmasya
glānir bhavati bhārata
abhyutthānam adharmasya
tadātmānaḿ sṛjāmy aham

"Whenever and wherever there is a decline in religious practice, O descendant of Bharata, and a predominant rise of irreligion — at that time I descend Myself."

Next we receive a nice description of Lord Bramha:
Lord Brahmā is one of the twelve authorities known as dvādaśa-mahājana (svayambhūr nāradaḥ śambhuḥ kaumāraḥ kapilo manuḥ/ prahlādo janako bhīṣmo balir vaiyāsakir vayam, Bhāg. 6.3.20). 

Brahmā receives knowledge from Kṛṣṇa and distributes that Vedic knowledge, and therefore he is an authority. There are four sampradāyas, or chains of disciplic succession, through which Vedic knowledge is distributed — one from Brahmā, one from Lakṣmī, one from Lord Śiva, and one from the four Kumāras. We have to approach an authoritative representative of Kṛṣṇa appearing in one of these sampradāyas, and then we can receive real knowledge. Thus the earth personified approached Brahmā, who prayed to the Supreme Personality of Godhead, "The world is now overburdened with demons, and therefore I request You to appear." Some say, therefore, that the Lord appeared at the request of Brahmā that He lighten the burden of the world.

We also have a nice description of Lord Narayana and the four symbols He holds in His four hands:
When Kṛṣṇa appears, He protects the devotees and kills the demons. Therefore Kṛṣṇa in His Nārāyaṇa form has four hands. In two hands He holds a disc and club with which to kill the demons, and in the other two hands He holds the conchshell and lotus with which to bless and protect the devotees.

Srila Prabhupada then give us Krishna's real reason for incarnating:
Now some may say that Kṛṣṇa appeared for this purpose or that purpose, but the real conclusion is that Kṛṣṇa appears for His own pleasure, not because He is bound by any other cause.

All glories to Sri Krishna and His servant, Srila Prabhupada!