A featured photo represents a gallery.
The default for non-password-protected galleries is to rotate randomly between all photos in your gallery. The default for password-protected galleries is to display a "Protected Gallery" graphic.
Later, if you select Remove Featured Photo, random rotation (or the "Protected Gallery" graphic) will return.
That's all there is to it.
What about categories and subcategories?
We'll use the featured thumbnail from the first gallery displayed inside that category or subcategory. To change it, you can always arrange your galleries.