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Bhagavad-ojtā  As It ls
[Ch 4]
paritrāṇāya sādhūnāṁ vināśāya ca duṣkṛtām dharma-saṁsthāpanārthāya sambhavāmi vuge vuge
paritrāṇāya —for the deliverance;  sādhūnām —of the devotees;  vināśāya —for the annihilation;  ca —also;  duṣkṛtām —of the miscreants;  dharma —principles of religion;  saṁsthāpana-arthāya —to reestablish;  sambhavāmi —I do appear;  yuge —millennium;  yuge —after millennium.
TRANSLATION
In order to deliver the pious and to annihilate the miscreants, as well as to reestablish the principles of religion, I advent Myself millennium after millennium.
PURPORT
According to  Bhagavad-gītā , a  sādhu  (holyman) is a man in Kṛṣṇa consciousness. A person may appear to be irreligious, but if he has the qualifications of Kṛṣṇa consciousness wholly and fully, he is to be understood to be a  sādhu . And  duṣkṛtam  applies to one who doesn't care for Kṛṣṇa consciousness. Such miscreants, or  duṣkṛtam , are described as foolish and the lowest of mankind, even though they may be decorated with mundane education; whereas another person, who is one hundred percent engaged in Kṛṣṇa consciousness, is accepted as  sādhu , even though such a person may neither be learned nor well cultured. As far as the atheistic are concerned, it is not necessary for the Supreme Lord to appear as He is to destroy them, as He did with the demons Rāvaṇa and Kamsa. The Lord has many agents who are quite competent to vanquish demons. But the Lord especially descends to appease His unalloyed devotees, who are always harassed by the demonic. The demon harasses the devotee, even though the latter may happen to be his kin. Although Prahlāda Mahārāja was the son of Hiraṇyakaśipu, he was nonetheless persecuted by his father; although Devakī, the mother of Kṛṣṇa, was the sister of Kamsa, she and her husband Vasudeva were persecuted only because Kṛṣṇa was to be born of them. So Lord Kṛṣṇa appeared primarily to deliver Devakī, rather than kill Kamsa, but both were performed simultaneously. Therefore it is said here that to deliver the devotee and vanquish the demon miscreants, the Lord appears in different incarnations.
In the  Caitanya-caritāmṛta  of Kṛṣṇadāsa Kavirāja, the following verses summarize these principles of incarnation: