The Mythological Amṛta
Amṛta (Sanskrit: a = not, mṛta = death — "that which does not die", immortality nectar) is the divine substance produced from the churning of the cosmic Kṣīrasāgara by the gods and demons. It is the source of the gods' immortality. The demon Rāhu disguised himself and drank some, was discovered by the Sun and Moon, and Viṣṇu cut off his head — which became the astronomical nodes (Rāhu and Ketu).
Viṣṇu himself as Mohinī (the enchantress form) distributed the amṛta exclusively to the gods, keeping it from the demons.
Theological Amṛta
The Sri Vaishnava tradition identifies three kinds of spiritual "amṛta":
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The Divine Name — the name Nārāyaṇa and all divine names are held to be immortality-nectar for the soul; they destroy the poison of saṃsāra and grant liberation
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The Divya Prabandham — Nammāzhvār describes his Tiruvāymozhi as amṛtam that he desires to share with the world; it is the nectar of devotion
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The Lord's prasāda — the food-offering (naivedyam) after it has been consecrated becomes prasāda — the Lord's own amṛta shared with the devotees; to partake of it is to receive the Lord's grace directly
Kārttika Month
The Kārttika month has special significance — the amṛta from the ocean-churning is associated with this month. Lighting a lamp and offering it to the Lord during Kārttika (the Dāmodara vrata) is said to grant the merit of offering amṛta.