It shows no increase in reputation of the asker, what is the purpose of being able to favorite questions? (clicking the star)
When you star a question you'll receive updates to it (edits, comments, and new answers). One use case is if you're interested in a question and wish to follow it's progress. By "starring" it you've bookmarked it and the system will provide updates to you in the StackExchange SuperCollider™ as if you were the owner of the question and a banner on the site when items change.