Grandma, please eat. Aunt/Uncle, please eat.
Children pay their respect to their elders and parents by acknowledging them at he table before they start eating. So I dont remember if yee ma (your aunt/my older sister) or die kow foo (your eldest uncle/my eldest brother) did it, but me and sigh kow foo (your younger uncle/my youngest brother) did it. Even today some of it still exists in Asia. I did it whenever people were around the table, doesnt matter few or a lot of people. I did every single meal, lunch, dinner, breakfast.
It means please eat, and then you go around the table. Even today, if youre invited to a luncheon or something, especially in Asia, I think here sometimes, the guest would say die gah sik fan (Everyone please eat), but its really a generational thing.
Definitely when I was little, in the family — not when we go out — at home I would specifically say po po sik fan (Grandma, please eat). It was required, if you dont do it you dont get to eat.
Theres only one major purpose, and that is to show respect to your elders. It means, help yourselves, lets eat.
The Chinese culture stresses the importance of respecting your elders, teaching children from a very young age to properly treat grandparents on first greeting, at the table, and when they receive gifts. My mother said she never taught my brothers and me this specific greeting because it was not as necessary. I think it happens much more between first-generation immigrants who have retained more traditional Chinese cultural values. To go around the entire table, asking each person to please eat means you presenting them with the first choice of food. This is an example of showing honor and love for your ancestors. It is a show of blessing as well.