Compassion as Divine Motive
Kāruṇya ('compassion,' 'mercy') is the Lord's affective response to the sight of suffering — particularly the sight of bound souls (baddha-jīvas) struggling in saṃsāra, ignorant of their own nature and of the Lord. The Viṣṇu Purāṇa and other texts describe the Lord as moved by kāruṇya when He sees even those who have long been heedless finally turning toward Him.
Kāruṇya and Kṛpā
Kāruṇya and kṛpā are often used interchangeably, but there is a nuance: kṛpā (grace) often refers to the Lord's gracious act of bestowing good without being asked; kāruṇya more specifically emphasizes the compassionate response to suffering — the seeing of the ārta (afflicted one) and being moved to help. Kāruṇya is thus the affective dimension of grace that responds specifically to distress.
Why the Lord Descends
The purpose of avatāras (divine descents) is intimately connected with kāruṇya: the Lord descends because He cannot bear to see His devotees and the world suffering under the weight of adharma and karmic bondage. The Bhagavad Gītā's declaration (yadā yadā hi dharmasya glānir bhavati) is an expression of this kāruṇya-driven intervention.
Kāruṇya and Prapatti
For the prapanna, the Lord's kāruṇya is the very foundation of confidence: even if one has accumulated heavy karma, even if one's qualifications are minimal, the Lord's kāruṇya — His inability to turn away from the genuinely surrendered — ensures protection. This is why the ācāryas can say: 'Surrender, and be certain of protection' — it is the Lord's kāruṇya that makes this certainty possible.