What does this light blue background mean?
Questions that have a tag that you marked as favorite (a.k.a. interesting, different parts of the interface use different names) are shown with a colored background (light blue on this site) in question lists. That's pretty much all that “favorite tag” does.
See What do the colors on Stack Overflow mean? for a list of colors that appear on Stack Overflow and their significance. This site is in beta, so it uses different colors, but the principle is the same.