Subscriptions allow users to receive an e-mail notification when a new post is added to the selected forum.
By clicking the (
) New subscription button, you can add a new e-mail address. If you check the Send confirmation e-mail to subscriber check-box on that page, the subscriber will receive a confirmation e-mail, telling them that they have been subscribed.
More resources can be found at Developer's Guide -> Modules -> Forums -> Overview.