Tarpaṇa is a term in the Vedic practice which refers to an offering made to divine entities. It refers to the act of the offering as well as the substance used in the offering itself. Tilatarpana is a different but associated term that is sometimes confused with Tarpana. Tilatarpana is a specific form of Tarpana involving libations offered to the Pitrs (deceased ancestors) using water and sesame seeds during Pitru Paksha or as a death rite.
(i) Tarpana means Arghya, an offering. It is offered to all devas as well as the Navagrahas whenever mulamantra is recited as japa. (ii) Instances of welcome Tarpana are:
(a) for Lakshmi, “आर्द्रां ज्वलंतीम् तृप्ताम् तर्पयन्तीम् “ Ārdrāṁ jvalantīm tr̥ptām tarpayantīm (Śrī Sūkta 4), "One who is satisfied and who satisfies those who offer Her Tarpana"
(b) for Tripura Sundari, bindu tarpaṇa santuṣṭām pūrvajā tripurāmbikā (Lalita Sahasranama 178, 974), "One who is satisfied by just a single drop of Tarpana"
(iii) Cow's milk (raw, unheated, and unpasteurized), water, sugar, saffron, cardamom, borneo-camphor, etc. are mixed and used as the offering according to the requirements.
(iv) One Tarpana (or Arghya) is offered for the recitation of every ten moolamantras and one for part thereof.