lokan vibhavayasi hamsi jagat pratipan
dharmam maha-purusa pasi yuganuvrttam
channah kalau yad abhavas tri-yugo ’tha sa tvam
Translation by His Divine Grace A. C. Bhaktivedanta Swami Srila Prabhupada:
In this way, my Lord, You appear in various incarnations as a human being, an animal, a great saint, a demigod, a fish or a tortoise, thus maintaining the entire creation in different planetary systems and killing the demoniac principles. According to the age, O my Lord, You protect the principles of religion. In the Age of Kali, however, You do not assert Yourself as the Supreme Personality of Godhead, and therefore You are known as Triyuga, or the Lord who appears in three yugas.
Purport by His Divine Grace A. C. Bhaktivedanta Swami Srila Prabhupada:
As the Lord appeared just to maintain Lord Brahma from the attack of Madhu and Kaitabha, He also appeared to protect the great devotee Prahlada Maharaja. Similarly, Lord Caitanya appeared in order to protect the fallen souls of Kali-yuga. There are four yugas, or millenniums — Satya, Treta, Dvapara and Kali. In all the yugas but Kali-yuga, the Lord appears in various incarnations and asserts Himself as the Supreme Personality of Godhead, but although Lord Sri Caitanya Mahaprabhu, who appears in Kali-yuga, is the Supreme Personality of Godhead, He never asserted Himself as such. On the contrary, whenever Sri Caitanya Mahaprabhu was addressed as being as good as Krsna, He blocked His ears with His hands, denying His identity with Krsna, because He was playing the part of a devotee. Lord Caitanya knew that in Kali-yuga there would be many bogus incarnations pretending to be God, and therefore He avoided asserting Himself as the Supreme Personality of Godhead. Lord Caitanya Mahaprabhu is accepted as the Supreme Personality of Godhead, however, in many Vedic literatures, especially in Srimad-Bhagavatam (11.5.32):
yajanti hi sumedhasah
In Kali-yuga, intelligent men worship the Supreme Personality of Godhead in the form of Sri Caitanya Mahaprabhu, who is always accompanied by His associates such as Nityananda, Advaita, Gadadhara and Srivasa. The entire Krsna consciousness movement is based on the principles of the sankirtana movement inaugurated by Sri Caitanya Mahaprabhu. Therefore one who tries to understand the Supreme Personality of Godhead through the medium of the sankirtana movement knows everything perfectly. He is sumedhas, a person with substantial intelligence.