- paritrāṇāya sādhūnāṁ
- vināśāya ca duṣkṛtām
- sambhavāmi yuge yuge
- (BG 4.8)
"In every millennium, every yuga . . ." There are different periods, just like in the whole year there are different periods in your country called summer, winter, fall, spring. They are coming by rotation. Similarly, there is rotation of time, which is divided into four millenniums called Satya-yuga, Tretā-yuga, Dvāpara-yuga and Kali-yuga.
So Kṛṣṇa says that dharma-saṁsthāpanārthāya sambhavāmi yuge yuge. Now, one may inquire that, "Kṛṣṇa appeared in the Tretā-yuga. And when He is going to appear in the Kali-yuga?" That is also mentioned in the Śrīmad-Bhāgavatam, that in the Kali-yuga there are three different incarnations mentioned in the Bhāgavatam or any other authentic Vedic literature. One incarnation is Lord Buddha, and another incarnation is Lord Caitanya, and another incarnation, in the last stage of this age, is Kalki, so far we get from the authority of Bhāgavatam.
So we have to accept according to the authentic scripture who is incarnation. We cannot accept anyone who claims that, "I am also incarnation." No. In the śāstras there are symptoms foretold of the incarnation. Just like about Lord Buddha there is mention, "In such and such place, in such and such form, in such and such activity, Lord Buddha will appear." Similarly, about Lord Caitanya is there. Similarly, there is a description about Kalki.