If you tap the star mark, that photo/video is added to your favorites. To view your favorites, go to the Collections screen by tapping the square icon at the top of the Album tab, then scroll down to Favorites. Only you can see which photos and videos you've marked as favorites.
Favorites also come in handy when creating photobooks. The app prioritizes your favorites when generating your monthly automatic photobook suggestion. When making a photobook, you can choose between viewing all photos or just your favorites during the photo selection step.