To grow means to "add more". If we are speaking in terms of human or animal growth, more cells are being added in order make that organism taller or larger. All organisms start as a single cell. That cell then undergoes mitosis (cellular division) time and time again. Even when an organism enters adulthood, the cells continue to divide.
(FYI- Development is not adding more cells, but changing the preexisting cells, such as during puberty.)
Synthesis, on the other hand, means "to make".
The two are related because proteins must be synthesized (hence the term "protein synthesis") using ribosomes. The proteins are then used to make cells and other cellular structures during periods of organismal growth and development.
Thus, cell structures must be synthesized. As more and more cells are synthesized, then growth occurs.