Gita 04.08 explained
vināśāya ca duṣkṛtām
sambhavāmi yuge yuge
Word for word:
paritrāṇāya — for the deliverance; sādhūnām — of the devotees; vināśāya — for the annihilation; ca — and; duṣkṛtām — of the miscreants; dharma — principles of religion; saṁsthāpana–arthāya — to reestablish; sambhavāmi — I do appear; yuge — millennium; yuge — after millennium.
To deliver the pious and to annihilate the miscreants, as well as to reestablish the principles of religion, I Myself appear, millennium after millennium.
When adharma arises or people who are adharmic arises or their count / power increases and they cause problem for dharmic people or make them stop dharma then to protect dharmic people and rise there dharma Lord comes example appearance of Lord Ram and Krishna.
Lord will destroy those who are demonic e.g. Lord Ram didn’t destroy Lanka but establishes rule of dharmic and devotee Vibhisana over there.
Srila Prabhupad talked about the primary purpose and secondary purpose of Lord’s appearance.
Avatarthi eiti avatar. That who descendants from spiritual realm to material realm.
There are various kinds of avatāras, such as puruṣāvatāras, guṇāvatāras, līlāvatāras, śakty-āveśa avatāras, manvantara-avatāras and yugāvatāras
Guna avatars are the incarnation of Lord who supervises the Guna or the modes of material nature. So for this Lord Brahma, Vishnu and Siva is there. Lord Siva is in charge of ignorance but he himself is not ignorant he is extremely powerful and also first class devotee Vaishanava nama Yatha Shanbu.
Lila avatar comes to perform lilas they may or may not teach yuga dharma, Yuga avatar is one you teaches yuga dharma. Also Yuga Dharma is taught in the beginning of yuga. But lila avatar can also teaches like Krishna teaches Bhagvad Gita and Uddav Gita etc. Also while demonstrating lila teaching will also go on.
Saktyavesa avatar -> living entity are empowered.
Manvantar avatar -> comes in every millennium. In region of every Manus.
Lord Chaitanys is mahavadanys he purifies miscreants.
Purpose of God coming here and destroying adharma is not that we stay here and enjoy this material world but purpose is that we go back home to Godhead. Yes God provides something by which our life is taken care of but the ultimate goal is that we go back to Godhead.