There are two types of subscriptions: Forum Subscriptions and Thread Subscriptions.
When you subscribe to a forum, you will be notified via email when any new thread is posted in the forum.
At the top of the forum list, you will find the link "Subscribe to this forum," which you can use to subscribe to the forum.
Forum subscriptions can be managed in the User CP.
Subscribing to a forum does not automatically subscribe you to all its subforums. you need to drill down to the subforum you are interested in and specifically subscribe to that subforum.
When you subscribe to a thread, you will be notified via email when a new reply has been posted in the thread. There will only be one notification per thread even though there may have been more than one reply after you "left" the forum. Once you visit the forum again, you will be able to receive notifications for that thread again. This "one-notification-per-thread-until-next-visit" concept is to prevent excessive spam, and conserve server resources.
At the bottom of any thread, you will find the link "Subscribe to this Thread," which you can use to subscribe to the thread.
You can also subscribe to threads when you make a reply. Select the "Email Notification" checkbox in the options when making your reply.
Thread subscriptions can be managed in the User CP as well.