What is that star below the number of votes in a question for? What happens when I star a question?
The tooltip says "Click to mark as favorite question". In your profile under "Activity" you have a "favorites" section. When you click the star on a question, it shows up there so you can find it again easily. You can click the star a second time to remove it from your favorites list.
If you end up with a long list of favorites, you can also search just the questions you've favorited using
infavorites:mine. The How do I search? page in the help center has more information.