The purpose of the pane is to list all the objects on the current page. You can then use the controls in the pane to hide or display the objects or to change the order in which they appear. Assuming there are objects listed for the current page, note that there is a small icon at the right of each object's name. Click this and you alternately hide or display the object.
When you select an object in the Selection and Visibility pane Word also selects it in the document itself. With an object selected you can adjust the ordering of that object, relative to other objects on the page, by clicking the up and down buttons at the bottom-right of the pane. Ordering only has practical value if your objects overlap each other in some manner; in that case the ordering determines which object is in front of or behind the other objects.
It should be noted that the Selection and Visibility pane displays only the objects on the currently displayed page, not all the objects in the document. This means that as you scroll through the document, what is listed in the pane will necessarily change as you move from page to page.