It happens that, in the guise of a devotee of God, I descend in person into the material universe, and more particularly in the age of Kali, where I appear as the son of Śacī in order to open the way to saṅkīrtana movement. (Brahma-yāmala)
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. (Ananta-saṁhitā)
Knowing that He [Lord Caitanya or Chaitanya] would be the Avatar for the age of Kali, the present age, sage Gargamuni had already predicted his coming at the ceremony where Kṛiṣhṇa received his name.
This child [Kṛiṣhṇa], now appeared with a transcendent dark complexion, affects three other skin tones, white, red, and yellow, depending on the age in which He manifests.
White, red and yellow, these are the three respective skin tones of the Lord, the bridegroom of the goddess of fortune, when He appears in the ages of silver, copper and iron. So, during the Copper Age, the Lord had appeared in a dark complexion (Black Blue) form.
In the Copper Age, the Supreme Lord appears in his dark complexion form. Dressed in yellow, he carries his personal weapons and adorns himself with the Kaustubah stone and the Śrīvatsa. These are the signs that characterize him.
The religion of the Iron Age consists in spreading the glories of the Holy Name. And this is the sole reason for the advent of the Lord in the form of Chaitanya, the Avatar of the golden complexion.
The Lord appears through the specific manifestations for each of the four ages. The Golden Age, the Silver Age, the Copper Age and the Iron Age. For each of these ages, the Avatar takes on a different complexion, respectively white, red, blue, black and yellow. In the Copper Age, for example, appeared Lord Krishna with a blue-black complexion, and in the Iron Age, Lord Chaitanya Mahaprabhu, with a yellow complexion. One should not regard the Lord as an Avatar like everyone else, but rather as the source of all Avatars.
Krishna claims to be the Father of all beings, and shows infinite goodness. This is why He descends into this world, to call to Himself fallen souls, souls conditioned by matter, to bring them back to their eternal home, to his kingdom, where they will live eternally with Him. To save these souls, Lord Krishna himself sometimes comes in his personal, original form, or as an Avatar. Sometimes He sends His intimate servants, His sons, His companions or even His qualified representatives, the authentic spiritual masters.