The keyboard shortcut for Select Children is Alt+Down (Windows) or (Mac). (Think “Down the family tree.”)
The children of an object are those objects that directly depend on the object. For example, a circle constructed by the Circle by Center+Radius command is a child of both the point and the segment used to define it.
If the selected object has no children, it remains selected. If the children of the selected object are hidden, then the selected object is deselected (leaving nothing selected).