While working on your document, you can show and hide AP elements manually, using the AP Elements panel, to see how the page will appear under different conditions.
An open eye means the AP element is visible.
A closed eye means the AP element is invisible.
If there is no eye icon, usually the AP element inherits visibility from its parent. (When AP elements are not nested, the parent is the document body, which is always visible.)
Also, no eye icon appears when no visibility is specified (which appears in the Property inspector as Default visibility).