In Hinduism, it is of great significance to offer food and water to dead ancestors on Amavasya (no moon day). The importance of offering food on Amavasya is found in the Garuda Purana
In the Garuda Purana (Preta khanda II 10.50-55) Lord Vishnu says to Garuda:
"On the day of Amavasya (new moon day), the airy manes (the ancestors) stand at the door of their descendents in order to receive their food. They remain there till sunset. When they do not receive their food they fall in despair and out of suffering heave long sighs and go back cursing the descendents. Therefore, one should carefully perform shraddha (offer food) to your ancestors on the new moon day (Amavasya) every month.
Some people are of the opinion that Pitra Puja should not be performed because the Atma or the deceased has already taken birth again. It might have been born as an animal, bird, insect, human form or whatever form that the soul would receive in accordance with the karmas (actions good or bad) of previous lives.
This argument has been refuted by scholars:
Every human being has to pay three debts with which he is reborn and that is (1) indebtedness to the Supreme Lord, (2) to the Rishis, and (3) to the forefathers.
Pitra Puja is a memorial service in which the devotee remembers as well as prays, addressing the departed he says: "O Pitrs in whichever form you may be, wherever you may be, we wish to remember and pray for your peace and welfare". Auspicious mantras are recited for the welfare, prosperity and peace of all beings.