When a person is subscribed to a forum it means that they will be sent email copies of every post in that forum (posts are sent about 30 minutes after the post was first written).
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).
Choosing the 'Everyone can choose to be subscribed' option 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').