Bhagavad Gita · Jnana Karma Sannyasa YogaChapter 4, Shloka 8 (4.8)

Three purposes.

1. Paritrāṇa — protection of the sādhūnām (the good). Shankaracharya: sādhūnāṃ san-mārga-sthānām — of those who walk the right path.
2. Vināśa — destruction of the duṣkṛtām. Shankaracharya: pāpa-kāriṇām — of those who do evil.
3. Dharma-saṃsthāpana — Shankaracharya: dharmasya samyak sthāpanam — the proper establishment of dharma.

Acharya Ramanuja — the tender meaning of "paritrāṇa". According to Ramanuja the sadhus are vaiṣṇavāgresarāḥ mat-samāśrayaṇe pravṛttāḥ — the foremost devotees, engaged in taking refuge in me; who, because my name, deeds and nature are avāṅ-manasa-gocara (beyond speech and mind), cannot even hold themselves together mad-darśanād ṛte — without seeing me — aṇu-mātra-kālam api kalpa-sahasraṃ manvānāḥ — who feel even a moment to be a thousand kalpas (aeons). Protecting them = mat-svarūpa-ceṣṭitāvalokanālāpādi-dānena — by giving them my own form, my divine play (leela), the sight of me and conversation with me. That is, the first purpose of the avatar is to give devotees his own presence. And kṣīṇasya vaidikadharmasya mad-ārādhana-rūpasya ārādhya-svarūpa-pradarśanena — establishing the Vedic dharma, which has declined and which consists in my worship, by showing the form of the one to be worshipped (me). Kṛta-tretādi-yuga-viśeṣa-niyamaḥ api nāsti — nor is there any rule tying it to a particular age (yuga).