The great sage Gargamuni had predicted his advent at the ceremony where Lord Krishna received his name, saying:
“This child [Kṛiṣhṇa], now appeared with a dark transcendental complexion, affects three other complexions, white, red, and yellow, according to the age in which He manifests Himself.”
White, red and yellow, these are the three respective carnations of the Lord, the husband of the goddess of fortune, when He appears in the ages of silver, copper and iron. Thus, during the Copper Age, the Lord appeared in a dark complexion form. Dressed in yellow, he wears his personal weapons and is adorned with stone Kaustubah and Śrīvatsa. These are the signs that characterize Him.
Lord Chaitanya Mahaprabhu appeared to spread the song of the holy name, to spread the love of God and to bring back fallen souls to him.
Krishna had said:
“I will appear in the holy land of Navadvīpa as the son of Śacīdevī.”
“When, in the Iron Age, the present age, comes the time to begin the movement of saṅkīrtana, (the collective song of the holy names of the Lord) I appear as the son of Śacīdevī.”
“It happens that, in the guise of a devotee of God, I come down in person into the material universe, and more particularly into the age of Kali (the Iron Age), where I appear as the son of Śacī to pave the way for sa mouvementkīrtana movement.”
“O Maheśvarī, the Supreme Lord, Kṛiṣhṇa himself, the very soul of Śrīmatī Rādhārāṇī and the master of the creation, maintenance and annihilation of the universe, descends into this world in the form of the Avatar of 'Gold.”
Raising his arms, singing the holy name and putting on all his loving gaze, He drives away all sins and submerges the beings with love for God.
These are the two reasons that made the Lord want to descend into this world: He wanted to taste the essence of the sweet feelings born of love for God and He wanted to spread the service of spontaneous devotion throughout the earth. So is the famous as the infinitely blessed and the most merciful.