Kāliya was a powerful, multi-hooded serpent who had taken up residence in the depths of the Yamunā river near Vṛndāvana, rendering the river's waters fatally poisonous. Birds flying overhead fell dead; animals drinking from the river perished. The young Kṛṣṇa, seeing the suffering of His beloved Vraja, leapt into the river, subdued Kāliya after a fierce battle, and danced upon his hoods (kāliya-mardana) — a display of divine mastery (aiśvarya) that caused the serpent's wives to pray for their husband's life and Kāliya himself to submit fully. Bhagavān then mercifully allowed Kāliya to leave for the ocean, granting him a boon of safety.
In Śrī Vaiṣṇava exegesis, the Kāliya episode carries deep allegorical significance. Kāliya's multiple hoods represent the many faces of ahaṅkāra (ego) and māna (pride). His poisoning of the Yamunā symbolizes how pride and self-will pollute the environment of devotion (bhakti-kṣetra). Kṛṣṇa's dance on his hoods is the divine grace (karuṇā) that subdues pride without destroying the soul — Kāliya is not killed but transformed and released. The serpent's wives' intervention models śarīrātma-bhāva: just as the body intercedes for its own continuance, the prapanna's nature pleads before Bhagavān.
The Tiruvāymozhi and Periya Tirumozhi make several references to Kāliya-mardana. The Āzhvārs see in Kṛṣṇa's feet resting on Kāliya's hood the image of total mastery of the material world, and they long for those same feet to rest upon their own heads (thiruvadi). This episode thus becomes a meditation on prapatti: the serpent who bows his hood is the devotee who surrenders completely, and the feet of Kṛṣṇa dancing upon that hood are the ultimate refuge.