I don't think I'm the best person to answer this because I've never set up a Mr. Linky. But, I think there is usually a little form to fill in with your name and a place to insert the address of the blog post for the book you reviewed. When you hit enter, a link will come up that directs people to your review...I think!
Tricia's got it right. It's a tool bloggers use because it is mostly super-convenient. It just asks folks for their name and their web address. Some weekly features like Poetry Friday and Thursday Thirteen and Wordless Wednesdays use them as well. When it comes to challenges, they can be useful to have folks signing up or to be used throughout the challenge to post links to their reviews. In these it might be name/book title or book title/name and then a link to your review.