yada yada hi dharmasya
glanir bhavati bharata
tadatmanam srjamy aham
"Whenever and wherever there is a decline in Dharma, O descendant of Bharata, and a predominant rise of adharma—at that time I descend Myself."
Yada yada = whenever, Dharmasya = dharma's, glani = ordeal or suffering, bhavati = happens, adharmasya = adharma, abhyutthanam = flourishes, tada = that time, , aham = I [Sri Krishna], srijami = create, atmanam = myself. Here we can not interpret atman as jeevatma as atman can never be created as it has no end. Also in the context He is not talking about other atman but about Himself and His birth. So we have to understand atman here refers to Himself. Srijami means creating. This is not the creation in the usual sense but His avatar, like Matsya or Koorma or Narsimha, etc,. Also, this Avatar He Himself decides and no other is involved. Thus, whenever righteousness has a suffering and unrighteousness flourishes, the Lord takes an avatar on Himself and descends to save dharma. It should be noted that He does not say He will appear when Dharma is destroyed but when suffering starts. Dharma is following the dos and don'ts of Vedas; and adharma is opposite. There is an interesting conversation between a Vishnu messenger and an Yama messenger in the story of Ajamilan. Though Ajamilan had accumulated papa or sins in his life, at the time of death he called his last child Narayana by that boy's name and those became his last words. So Vishnu messengers said that Ajamilan was to be taken to the world of Vishnu, while Yama messengers disputed saying that for the sins he committed he had to be taken to hell or Narak only. Yama's messengers say that whatever is agreed to by Vedas are all Dharma and whatever discarded by Vedas are all adharma. Dharma protects the world. If we protect Dharma it will in turn protect us. Our culture and tradition is sanathana or very ancient Dharma. Speak truth, help others, be not selfish, atman is different from body, rebirth is there, believe in God and be devoted, etc., are all ancient Dharma, we have been following. Whenever this Dharma is harassed the Lord appears. We can remember the avatars like Sri Narasimha, Sri Thrivikrama and the story of Gajendra. In the first case the devotee was made to suffer. In the next, another's property was grabbed. In the last He had to appear to save a devotee who staunchly believed that he would be rescued by the Lord.