When a person is subscribed to a forum it means that they will be sent email copies of every subsequent post in that forum. Posters have 30 minutes by default to edit their post before it is sent though this time limit can be changed by an Administrator.
People can usually choose whether or not they want to be subscribed to each forum. However, if a teacher forces subscription on a particular forum then this choice is taken away and everyone in the class will get email copies.This is especially useful in the News forum and in forums towards the beginning of the course (before everyone has worked out that they can subscribe to these emails themselves).
Note that even if you force subscriptions every user can disable all email from Moodle by editing the settings in their profile, or elect to have all email sent once a day in a digest contain either all posts or simply the subject headings.
Choosing Everyone can choose to be subscribed enables you to check (and modify) the number of subscribers ('Show/edit current subscribers') and to subscribe to (or unsubscribe from) the forum ('Subscribe to this forum' / 'Unsubscribe from this forum').