A Child Graphic refers to the Graphic object that is used to hold display information for non-Column children of a Table that are displayed inside a Table in a Diagram. See Diagram Display Options for more details. For example, you could choose to display Key Constraints inside a Diagram Table. If you do so, a Child Graphic object will be created for each displayed key. Each of these Child Graphic Objects will inherit from a Child Graphics Template. Which Child Graphics Template it will initially inherit from depends on the type of object it is. You can specify that a Child Graphics Template is the default for different object types in the Child Graphics Template property tab:
This screenshot shows that I have a Child Graphics Template called "Child Graphics Template for Keys" and made it the default for Key Constraints. Now if I chose to display Key Constraints inside a Diagram Table, they will automatically be set to inherit from this Template, and hence be displayed red and bold.