This character is made up of two words, lau (老 old, or aged) on top of zi (子 young, or offspring). Lau refers to our parents, zi refers to ourselves. There is a bond between the two. If we, as much as, feel that there is a generation gap between our parents and ourselves, we are already not being filial!
The word also signifies infinite past and infinite future: before us there are our parents, grandparents and so on. Looking into the future, there are our children, grandchildren...
A child's duty is to be filial. It is not only limited to physical and mental care of one's parents. The ultimate filial piety is for us to achieve enlightenment ourselves, that is, to fully understand the true nature of the universe. Our parents will also, by virtue of our achievement, blessed with peace and happiness.
Hence, the foundation of Buddhism is built on filial piety.