The Confidential Reasons for the Lord's Appearance

CC Adi 4.16
The Lord’s desire to appear was born from two reasons:

•  the Lord wanted to taste the sweet essence of the mellows of love of God,
•  and He wanted to propagate devotional service in the world on the platform of spontaneous attraction.   

 
CC Ādi 4.230 "Desiring to understand the glory of Rādhārāṇī’s love, the wonderful qualities in Him that She alone relishes through Her love, and the happiness She feels when She realizes the sweetness of His love, the Supreme Lord Hari, richly endowed with Her emotions, appeared from the womb of Śrīmatī Śacī-devī, as the moon appeared from the ocean.”



From the Introduction to Adi Chapter 4- 3 reasons for the Lord's appearance

In this chapter of the epic Caitanya-caritāmṛta, Kṛṣṇadāsa Kavirāja Gosvāmī has stressed that Lord Caitanya appeared for three principal purposes of His own. 

1. The first purpose was to relish the position of Śrīmatī Rādhārāṇī, who is the prime reciprocator of transcendental love of Śrī Kṛṣṇa. Lord Kṛṣṇa is the reservoir of transcendental loving transactions with Śrīmatī Rādhārāṇī. The subject of those loving transactions is the Lord Himself, and Rādhārāṇī is the object. Thus the subject, the Lord, wanted to relish the loving mellow in the position of the object, Rādhārāṇī.
2. The second reason for His appearance was to understand the transcendental mellow of Himself. Lord Kṛṣṇa is all sweetness. Rādhārāṇī’s attraction for Kṛṣṇa is sublime, and to experience that attraction and understand the transcendental sweetness of Himself, He accepted the mentality of Rādhārāṇī.
3. The third reason that Lord Caitanya appeared was to enjoy the bliss tasted by Rādhārāṇī. The Lord thought that undoubtedly Rādhārāṇī enjoyed His company and He enjoyed the company of Rādhārāṇī, but the exchange of transcendental mellow between the spiritual couple was more pleasing to Śrīmatī Rādhārāṇī than to Śrī Kṛṣṇa. Rādhārāṇī felt more transcendental pleasure in the company of Kṛṣṇa than He could understand without taking Her position, but for Śrī Kṛṣṇa to enjoy in the position of Śrīmatī Rādhārāṇī was impossible because that position was completely foreign to Him. Kṛṣṇa is the transcendental male, and Rādhārāṇī is the transcendental female. Therefore, to know the transcendental pleasure of loving Kṛṣṇa, Lord Kṛṣṇa Himself appeared as Lord Caitanya, accepting the emotions and bodily luster of Śrīmatī Rādhārāṇī.

Lord Caitanya appeared in order to fulfill these confidential desires, and also to preach the special significance of chanting Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, Hare Hare/ Hare Rāma, Hare Rāma, Rāma Rāma, Hare Hare and to answer the call of Advaita Prabhu. These were secondary reasons.