This text is from Śrīmad-Bhāgavatam (SB 11.5.32). Śrīla Jīva Gosvāmī has explained this verse in his commentary on the Bhāgavatam, known as the Krama-sandarbha, wherein he says that Lord Kṛṣṇa also appears with a golden complexion. That golden Lord Kṛṣṇa is Lord Caitanya, who is worshiped by intelligent men in this age. That is confirmed in Śrīmad-Bhāgavatam by Garga Muni, who said that although the child Kṛṣṇa was blackish, He also appears in three other colors—red, white and yellow. He exhibited His white and red complexions in the Satya and Tretā ages respectively. He did not exhibit the remaining color, yellow-gold, until He appeared as Lord Caitanya, who is known as Gaura Hari.
Śrīla Jīva Gosvāmī explains that kṛṣṇa-varṇam means Śrī Kṛṣṇa Caitanya. Kṛṣṇa-varṇa and Kṛṣṇa Caitanya are equivalent. The name Kṛṣṇa appears with both Lord Kṛṣṇa and Lord Caitanya Kṛṣṇa. Lord Śrī Caitanya Mahāprabhu is the Supreme Personality of Godhead, but He always engages in describing Kṛṣṇa and thus enjoys transcendental bliss by chanting and remembering His name and form. Lord Kṛṣṇa Himself appears as Lord Caitanya to preach the highest gospel.
Lord Caitanya always chants the holy name of Kṛṣṇa and describes it also, and because He is Kṛṣṇa Himself, whoever meets Him will automatically chant the holy name of Kṛṣṇa and later describe it to others. He injects one with transcendental Kṛṣṇa consciousness, which merges the chanter in transcendental bliss. In all respects, therefore, He appears before everyone as Kṛṣṇa, either by personality or by sound. Simply by seeing Lord Caitanya one at once remembers Lord Kṛṣṇa. One may therefore accept Him as viṣṇu-tattva. In other words, Lord Caitanya is Lord Kṛṣṇa Himself.
Sāṅgopāṅgāstra-pārṣadam further indicates that Lord Caitanya is Lord Kṛṣṇa. His body is always decorated with ornaments of sandalwood and with sandalwood paste. By His superexcellent beauty He subdues all the people of the age. In other descents the Lord sometimes used weapons to defeat the demoniac, but in this age the Lord subdues them with His all-attractive figure as Caitanya Mahāprabhu. Śrīla Jīva Gosvāmī explains that His beauty is His astra, or weapon, to subdue the demons. Because He is all-attractive, it is to be understood that all the demigods lived with Him as His companions. His acts were uncommon and His associates wonderful. When He propagated the saṅkīrtana movement, He attracted many great scholars and ācāryas, especially in Bengal and Orissa. Lord Caitanya is always accompanied by His best associates like Lord Nityānanda, Advaita, Gadādhara and Śrīvāsa.