yadā yadā hi dharmasya
glānir bhavati bhārata
abhyutthānam adharmasya
tadātmānaḿ sṛjāmy aham

Translation of Bhagavad Gita 4.7

Whenever and wherever there is a decline in religious practice, O descendant of Bharata, and a predominant rise of irreligion—at that time I descend Myself.

Commentary by Sri Vishvanatha Chakravarthi Thakur of Gaudiya Sampradaya:

When do I appear?” This verse answers.

I appear when I cannot tolerate both the destruction (glani) of dharma and the increase (abhyutthanam) of adharma, in order to reverse   the   situation.   I   create   my   body   (atmanam). Madhusudana Sarasvati says, “I show that body which exists eternally, as if it were created by my energy.”

Commentary by Sri Ramanuja of Sri Sampradaya:

4.7 There is no restriction as to the time of My birth; whenever the Dharma taught by the Vedas that must be observed according to the arrangements of the four stations and the four stages of life declines, and Adharma, its opposite, increases, then I Myself, by My own will and in the manner stated, incarnate Myself. Sri Krsna gives the purpose of His birth.

Commentary by Sri Sridhara Swami of Rudra Sampradaya:

Anticipating the question of exactly when is it that He manifests Himself, Lord Krishna declares unequivocally beginning with the words yada yada meaning whenever and wherever. Whenever there is a decline in righteous and wherever there is a predominance of unrighteousness.

Commentary by Sri Madhvacharya of Brahma Sampradaya:

Sri Madhvacharya did not comment on this sloka.

Commentary by Sri Keshava Kashmiri of Kumara Sampradaya:

So it is accepted that Lord Krishna has no beginning and is immutable and that He instructed Visvavan the demi-god of the sun millenniums before in a past incarnation but a question may arise in regard to the many births. When did all these manifestations take place? Lord Krishna clears up this point beginning with the words yada yada meaning whenever and wherever. This signifies that anytime or anyplace that a decline in righteousness is apparent, being antagonistic and in opposition to divinity, at that time the Supreme Lord manifests Himself. Here the word dharma which means righteousness does not imply ordinary righteousness as applies to the mundane interactions of varnasrama or the position and stages in life. Here dharma applies to the deterioration of bhakti yoga or the science of the individual consciousness attaining communion with the ultimate consciousness by the means of loving devotion. When there is a decline in bhakti yoga and the path of devotion to God is opposed by unrighteous rulers who in ignorance are inimical to love of God then at that time Lord Krishna manifests Himself personally. Thus it is stated by Bhumi the goddess of the Earth in the Brahmavaivarta Purana: The Earth is unable to bear the burden of those greatly sinful persons who are averse to devotion to Lord Krishna and who blaspheme Lord Krishna’s devotees. Lord Krishna has explained in the Srimad Bhagavatam that when sattva guna or the mode of goodness increases then humans naturally will proportionately increase in righteousness and devotion to Him. A person living their life without any devotion to God has wasted there human existence and a person who does not take delight in hearing about the sublime transcendental pastimes of the Suprem Lord Krishna which benefits all living entities has lived their life in vain.

Commentary by Sri Adi Shankaracharya of Advaita Sampradaya:

4.7 O scion of the Bharata dynasty, yada yada hi, whenever; bhavati, there is; a glanih, decline, decrease; dharmasya, of virtue consisting of the duties of castes and stages of life of living beings, which are the means to achieving properity and Liberation; and abhyutthanam, increase, rise; adharmasya, of vice; tada, then; do aham, I; srjami, manifest; atmanam, Myself, through Maya. Why?

Commentary by Sri Abhinavagupta of Kaula Tantra Sampradaya:

4.5-9 Bahuni etc. upto Arjuna. Indeed the Bhagavat is Himself devoid of all bodily connections on account of His having the group of the ‘six attributes’ in toto. Yet, out of His nature of stabilising [the universe], and out of compassion, He sends forth (or creates) that is which the Self is secondary. The meaning is this : He takes hold of a body, in which the Self, with the group of ‘six qualities’ in full, remains secondary because of Its role as a helper of the body. On account of this, His birth is divine. For, it has been created not by the results of actions, but by His own Trick-of-Illusion, by the highest knowledge of Yoga, and by the energy of Freedom of His own. His action too is divine, as it is incabable of yielding fruits [for Him]. Whosoever knows this truth in this manner i.e., realises in his own Self also in this manner, he necessarily understands the Bhagavat Vasudeva beng.

Sanskrit Shloka Without Transliteration Marks:

yada yada hi dharmasya
glanir bhavati bharata
abhyutthanam adharmasya
tadatmanam srjamy aham

Sanskrit to English Word for Word Meanings:

yadā yadā — whenever and wherever; hi — certainly; dharmasya — of religion; glāniḥ — discrepancies; bhavati — become manifested; bhārata — O descendant of Bharata; abhyutthānam — predominance; adharmasya — of irreligion; tadā — at that time; ātmānam — self; sṛjāmi — manifest; aham — I.