The Notify button enables registered members to subscribe to email notification of replies to topics in this board.
Basically, that means that if you click the button that says "notify," you will be notified by email when a new post has been made on the thread that interests you. Some people really, really like the feature. Others do not. That's why it's optional.
Also, when you start a new thread, you have the option to check the "notify me of replies" box. That will do the same thing as clicking the "notification" button.