When you want to get notifications about anything happening (i.e. a new topic or reply) in a forum you want use the Subscribe To Forum feature. For example, if you want to stay informed about General Discussion forum as shown here without having to login to the site, setting this feature to subscribe will send you a notification and link when a new topic is created or replies to existing topics are made.
Here is how you subscribe to a forum (go to the forum you want first).
If you are either no longer interested in getting notifications from a forum that you are subscribed to or perhaps you are getting flooded with email because of too much activity, you can also unsubscribe from the forum.
Here is how you unsubscribe from a forum (go to the forum you want first).
Please note that unsubscribing from a forum will NOT also unsubscribe you from a specific topic(s) – the integrity of subscriptions are not affected in this case.