As with many other contemporary beliefs, the Buddha ethicized Brahmanical ideas about the afterlife, and shifted the practices associated with them from the material to the psychological. He reinterpreted the ‘fathers’ (pita) as the ‘hungry spirits’ (peta) and said that only greedy, immoral or wicked people might get reborn as such unhappy beings (A.I,155). A good and kindly person, he said, would probably be reborn as a human or in heaven, rather than the world of the fathers. When the brahman Janussoni asked if it were really possible for the departed to receive and benefit from the material offerings made to them the Buddha replied that this could only happen if they had been reborn as a hungry spirit (A.V,269).
However, it seems unlikely that the Buddha would have believed the rather primitive notion that material offerings could actually be conveyed to another dimension. More likely the Buddha was using skillful means, adopting or taking into account the questioner’s standpoint in order to speak to him or her in terms they could understand. In this case he probably did so because although he would not have accepted that material things can be conveyed to another world, he could see that Janussoni’s desire to do so was based on good intentions -love, gratitude and concern for his departed ancestors. When the Buddha was addressing his instructed disciples he would say that the best way they could give their departed relatives something that would benefit them would be to lead a good and moral life here and now. Once he said: ‘If a monk should wish, “Those departed relatives and ancestors of mine who I recall with a calm mind, may they enjoy great fruit and benefit,” then he should be one who is filled with virtue, who spends time in solitude, dedicated to meditation and calmness of mind.’ (A.V,132). The Buddha’s idea seems to have been that if you wish to give happiness to your departed loved ones lead a life of kindness and integrity.
In keeping with this interpretation the Kathavatthu specifically denies that the departed can receive or benefit from material things offered to them (Kv. XX,4).
In traditional Buddhists countries today people will do good deeds, usually making offerings to monks, and then in a simple ceremony dedicate the merit they have created to their departed loved ones. Although people are told by monks and often believe that they actually ‘transfer the merit’ to their departed loved ones this is a misunderstanding of Buddhist doctrine. See http://www.buddhisma2z.com/ under Merit and Transference of Merit. The picture shows a supposed ‘merit-making’ ceremony.