Young multicelled organisms usually start out small, then grow in size, and increase in complexity. What is this process called?
There are actually several processes that are a part of this definition, and the specific one this answer is looking for is probably more apparent within the context of your particular textbook or classroom.
Growth in size is governed largely by mitosis, the process of cell replication, and the relationship of mitosis to cell death. An organism that undergoes mitosis more rapidly than it loses cells through death could be said to be growing.
Undergoing cell differentiation (which is, basically, an increase in complexity) is an aspect of both mitosis and epigenetics, in which cells are programmed according to the demands of different body tissues, altering their gene expression. This is what results in a skin cell being different from a bone cell, and both cells producing only more cells of their own type.
These events are collectively considered "growth and development."