This forgetfulness was so overwhelming that Advaita Prabhu was convinced that no one but Lord Kṛṣṇa Himself could enlighten people about devotional service to the Supreme Lord. Therefore Advaita requested Lord Kṛṣṇa to appear as Lord Caitanya. Offering tulasī leaves and Ganges water, He cried for the Lord’s appearance. The Lord, being satisfied by His pure devotees, descends to satisfy them. As such, being pleased by Advaita Ācārya, Lord Caitanya appeared.
(CC Adi 3 Summary)

Advaita Acārya having appeared, He found the world devoid of devotional service to Śrī Kṛṣṇa because people were engrossed in material affairs. Everyone was engaged in material enjoyment, whether sinfully or virtuously. No one was interested in the transcendental service of the Lord, which can give total relief from the repetition of birth and death. Seeing the activities of the world, the Acārya felt compassion and began to ponder how He could act for the people's benefit. [Advaita Acārya thought:] "If Śrī Kṛṣṇa were to appear as an incarnation, He Himself could preach devotion by His personal example. "In this Age of Kali there is no religion other than the chanting of the holy name of the Lord, but how in this age will the Lord appear as an incarnation? "I shall worship Kṛṣṇa in a purified state of mind. I shall constantly petition Him in humbleness. "My name, 'Advaita,' will be fitting if I am able to induce Kṛṣṇa to inaugurate the movement of the chanting of the holy name." While He was thinking about how to propitiate Kṛṣṇa by worship, the following verse came to His mind. "Śrī Kṛṣṇa, who is very affectionate toward His devotees, sells Himself to a devotee who offers Him merely a tulasī leaf and a palmful of water." Advaita Acārya considered the meaning of the verse in this way: "Not finding any way to repay the debt He owes to one who offers Him a tulasī leaf and water, Lord Kṛṣṇa thinks, 'There is no wealth in My possession that is equal to a tulasī leaf and water.' "Thus the Lord liquidates the debt by offering Himself to the devotee." Considering in this way, the Acārya began worshiping the Lord. Thinking of the lotus feet of Śrī Kṛṣṇa, He constantly offered tulasī buds in water from the Ganges. He appealed to Śrī Kṛṣṇa with loud calls and thus made it possible for Kṛṣṇa to appear. Therefore the principal reason for Śrī Caitanya's descent is this appeal by Advaita Acārya. The Lord, the protector of religion, appears by the desire of His devotee. "O my Lord, You alwa\ys dwell in the vision and hearing of Your pure devotees. You also live in their lotuslike hearts, which are purified by devotional service. O my Lord, who are glorified by exalted prayers, You show special favor to Your devotees by manifesting Yourself in the eternal forms in which they welcome You." The essence of the meaning of this verse is that Lord Kṛṣṇa appears in all His innumerable eternal forms because of the desires of His pure devotees. Thus I have surely determined the meaning of the fourth verse. Lord Gaurāńga [Lord Caitanya] appeared as an incarnation to preach unalloyed love of God.
(CC Adi 3.96 - 3.113)

The most merciful Lord Viśvambhara looked at Advaita and spoke as follows. I have descended to fulfill Your vow, for You have profusely worshiped Me. I was sleeping in the ocean of milk, but Your loud cries broke My sleep. You could not tolerate the suffering of the living entities, so You have brought Me to deliver them. All My associates that You saw surrounding Me have already taken birth because of You. By Your mercy, Vaiṣṇavas that even personalities like Brahmā desire to see will now be seen by everyone. On hearing the Lord’s words, Advaita and His wife raised their arms and began to cry. Today My life has become successful. Today all My desires have been fulfilled. Today My life and activities have become successful for I have seen Your lotus feet. The four Vedas only describe Your glories but cannot directly see You. Yet You have appeared because of Me. I have no power outside of Your causeless mercy. Who can deliver the living entities other than You? While speaking in this way, Advaita Ācārya floated in the ecstasy of love of God. The Lord then said, “Now arrange for My worship.” On receiving the Lord’s order, He happily worshiped the lotus feet of Lord Caitanya with full attention.
(Śrī Caitanya-bhāgavata, Madhya-khaṇḍa 6.093 – 6.105)

Lord Advaita Ācārya is the incarnation of Mahā-Viṣṇu, whose main function is to create the cosmic world through the actions of māyā.
(CC Ādi 6.4)

Because He is nondifferent from Hari, the Supreme Lord, He is called Advaita, and because He propagates the cult of devotion, He is called Ācārya. He is the Lord and the incarnation of the Lord’s devotee. Therefore I take shelter of Him.
(CC Ādi 6.5)

Śrī Advaita Ācārya is indeed directly the Supreme Personality of Godhead Himself. His glory is beyond the conception of ordinary living beings.
(CC Ādi 6.6)

Mahā-Viṣṇu performs all the functions for the creation of the universes. Śrī Advaita Ācārya is His direct incarnation.
(CC Ādi 6.7)

Being a reservoir of all auspicious attributes, Śrī Advaita Ācārya is all-auspicious for the world. His characteristics, activities and name are always auspicious.
(CC Ādi 6.12)

In the form of Advaita He infuses the material ingredients with creative energy. Therefore, Advaita is the original cause of creation.
(CC Ādi 6.20)

Śrī Advaita Ācārya is the creator of millions and millions of universes, and by His expansions [as Garbhodakaśāyī Viṣṇu] He maintains each and every universe.
(CC Ādi 6.21)

Śrī Advaita is the principal limb [aṅga] of Nārāyaṇa. Śrīmad-Bhāgavatam speaks of “limb” [aṅga] as “a plenary portion” [aṁśa] of the Lord.
(CC Ādi 6.22)

It is through Him [Advaita Ācārya] that Lord Caitanya spread the saṅkīrtana movement and through Him that He delivered the world.
(CC Ādi 6.35)

The glory and attributes of Advaita Ācārya are unlimited. How can the insignificant living entities fathom them?
(CC Ādi 6.36)

Śrī Advaita Ācārya is a principal limb of Lord Caitanya. Another limb of the Lord is Nityānanda Prabhu.
(CC Ādi 6.37)

Thinking “He [Śrī Advaita Ācārya] is a disciple of Śrī Mādhavendra Purī,” Lord Caitanya obeys Him, respecting Him as His spiritual master.
(CC Ādi 6.40)

To maintain the proper etiquette for the principles of religion, Lord Caitanya bows down at the lotus feet of Śrī Advaita Ācārya with reverential prayers and devotion.
(CC Ādi 6.41)

Śrī Advaita Ācārya, however, considers Lord Caitanya Mahāprabhu His master, and He thinks of Himself as a servant of Lord Caitanya Mahāprabhu.
(CC Ādi 6.42)

He forgets Himself in the joy of that conception and teaches all living entities, “You are servants of Śrī Caitanya Mahāprabhu.”
(CC Ādi 6.43)

The conception of servitude to Śrī Kṛṣṇa generates such an ocean of joy in the soul that even the joy of oneness with the Absolute, if multiplied ten million times, could not compare to a drop of it.
(CC Ādi 6.44)

Out of His causeless mercy upon Me, Advaita Ācārya has also come here. I am indebted to Him for His affectionate behavior. This debt is impossible for Me to liquidate.
(CC Antya 12.70)

All glories to Advaita Prabhu, the incarnation of the Supreme Personality of Godhead! He induced Kṛṣṇa to descend and thus delivered the entire world.
(CC Antya 8.4)

After this incident the Lord blessed Haridāsa Ṭhākura and vanquished the offense of His mother at the home of Advaita Ācārya.
PURPORT
On the mahā-prakāśa day, Lord Caitanya Mahāprabhu embraced Haridāsa Ṭhākura and informed him that he was none other than an incarnation of Prahlāda Mahārāja. When Viśvarūpa took sannyāsa, Śacīmātā thought that Advaita Ācārya had persuaded Him to do so. Therefore she accused Advaita Ācārya of this, which was an offense at His lotus feet. Later Lord Caitanya induced His mother to take the dust of Advaita Ācārya’s lotus feet, and thus her vaiṣṇava-aparādha was nullified.
(CC Adi 17.71)