When you reply to a thread, it subscibes you by default, you are automatically subscribed (with no email notification). You can change this default behavior by changing the subscription option - it's just below the Manage Attachments button.
You can also subscribe to a thread you haven't posted in by choosing "Subscribe to this thread" option under "Thread Tools".
When you are subscribed, threads with new replies show up in your
user control panel. This way, you have an easy view into which threads have new posts that you are interested in.
If you at some point have less time to come by the board and look for new posts, but you are interested in a particular topic, you can subscribe with email notification - so anytime a particular thread gets updated you get an e-mail letting you know. The options allow for instant, daily, or weekly notification.
You can also subscribe to forums. When you do that, you can check the box on the realtime posts page to only see new posts in forums that you subscribe to. It makes the list a little bit cleaner when the board is hopping.
There's also a tie-in to RSS Feeds so you can see updates and threads within something like
Google Reader, but I haven't really exposed those just yet.
Unfortunately, with quick reply, you don't get a chance to change your subscription settings.