Generally speaking, in China when a person dies, the name of the deceased is inscribed on paper or white cloth and places in front of the coffin. After burial the inscription is brought home and placed on the family altar. In time, a "spirit tablet" is created. The front of this piece of wood is inscribed the name, family and social rank of the deceased and on the back the date of birth and death are written. The tablet represents the deceased. Some believe that the soul of the deceased resides in the tablet. At proper times, family members perform acts of veneration by kowtowing, burning incense and making offering of food and drink, etc.
The most fundamental aspect of Ancestor worship is the belief that life continues after death and that a relationship with the living is maintained. It is a way of honoring those who have passed beyond the visible world and of linking the past with the present generation.
Matteo Ricci viewed Ancestor Worship as an expression of "Filial Piety". He did not think this was idolatry because they do not think the dead would eat the offered food nor did they ask anything from their ancestors nor did they think of them as being divine. He was also aware that some practices were superstitious so his converts were only allowed to practice Ancestor worship if it was free of superstitions.
In 1715 Pope Clement XI issued a decree declaring that Catholics were not allowed to practice Ancestors Worship because, he said, that they were pagan rituals.
In 1932-33 events in Japan and Manchuria forced a reconsideration of Ancestor worship. The Propaganda Fide with the approval of Pope Pius XII issued a declaration which allowed Catholics to participate in public honors to Confucius and that signs of respect toward the ancestral tablets were lawful and honorable. If the public functions appeared superstitious, Catholics should maintain a passive attitude.
In 1939 Pope Pius XII gave formal permission for Chinese Catholics to participate in honoring their ancestors. Fr. Kimm points our that worship is reserved to God alone. Ancestral ceremonies simply express the love and respect for those who helped us make us what we are today. "If we forget them, we forget ourselves."
Love and respect fits into the Catholic faith. Since God is the origin of all life, reverence for our ancestors is really reverence for God. It is an expression of the commandment to love our mother and father. As Catholics we believe that when people die they become part of the Communion of Saints. The deceased who share God's life in heaven remain involved in the lives of those who struggle on earth.(Webpage: Why do Chinese people honor ancestors?
Fr. Kimm )
The Vietnamese bishops have also included the ancestor concept in the Second Eucharist Prayers as follows: "Remember also the faithful, our brothers and sisters, who rest in peace in the expectation of the resurrection, and the dead who can only trust in your mercy. Remember in particular our ancestors, our parent and our friends who have left this world...." They've also included the concept in the various prayers of the Tet (New Year) liturgy.