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 15 minutes after the post was first written).
People can usually choose whether or not they want to be subscribed to each forum.
However, if you choose to force subscription on a particular forum then all course users will be subscribed automatically, even those that enrol at a later time.
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).
If you choose the option "Yes, initially" then all current and future course users will be subscribed initially but they can unsubscribe themselves at any time. If you choose "Yes, forever" then they will not be able to unsubscribe themselves.
Note how the "Yes, initially" option behaves when you update an existing forum: Changing from "Yes, initially" to "No" will not unsubscribe existing users, it will only affect future course users. Similarly changing later to "Yes, initially" will not subscribe existing course users but only those enrolling later.