Amṛta (Amrita) was one of the Aṣṭottara Sahasranāma (Ashtottara Sahasranama; Thousand and Eight Names) of Śiva (Siva). In Śivasahasranāmastotra (Sivasahasranamastotra), he is twice addressed by this name. After Samudramanthana (the churning of ocean), Dhanvantari came out of the ocean, carrying a pitcher full of Amṛta (amrita; nectre). Amṛta is that elixir which is desired by both Gods and Asuras, which gives immortality. Mahādeva (Mahadeva) is the manifestation of this Amṛta, so he is called by this name —
amṛta sudhārpaḥ.
Mṛta (Mrita) means dead, so Amṛta refers to someone who is beyond death. Mahādeva is immortal, he has no decay or decline, so Amṛta is one of his names –
amṛto maraṇavarjitaḥ.