The Outliner is designed to be able to display a 'heirarchy' of information, that is, data that belongs to other data, including parent/child relationships.
To expand the Outliner heirarchy press the '+' (which changes to a '-' when clicked) next to the parent object:
You now have access to the selection, render and viewport visibility properties of the child object.
You can also press Numpad + or Numpad - to expand or collapse levels of the Outliner (while the cursor is in the Outliner) for multiple objects.
See the Outliner page in the Blender Manual for more information: