Logged-in members can mark songs with a star. Starring a song is similar to indicating "like" or "favorite" or "in my repertoire." Songs will then appear higher in searches for members who have starred them. Additionally, the more popular a song is (i.e. the more it has been starred) the earlier it will be returned in everyone's searches so by starring a songs you are making Word to Worship better.
To mark a song with a star simply click on the gray star to the right of the song title. Clicking a yellow star subsequently removes the star and it becomes gray again.