Subscriptions give you notifications when someone posts to a thread you are subscribed to. You will also get a list of threads you are subscribed to in your User CP (see below). Subscriptions can also notify you by either a private message or email notification when someone replies to a thread you are subscribed to. You can change this settings globally or on a per thread basis. It is similar to the context of tagging yourself in Facebook on a post. You will get notification for replies on that post, etc.

• Instant PM notification: You will get a private message every time someone replies to a thread you posted in
• Email notification: You will get an email every time someone replies to a thread you posted in
• No notification: You will subscribe to all threads that you posted in, but you will not get any notifications.
• Do not subscribe:. You will not subscribe to anything automatically.

Global Subscriptions: You can change this setting at User CP -> Edit Options -> Default Thread Subscription Mode. This option reflects your subscriptions globally. This will automatically effect you to any threads you subscribe/unsubscribe to from thereafter.

Subscriptions on a per thread basis: In your reply post editor, there is a checkbox for thread subscription with similar options. This will reflect by default your choice automatically of your global option set. You can choose to modify a specific thread to a subscription choice on a per thread basis regardless of your global subscription options.

Subscribe to a thread you have not posted on: If you are not posting on a thread and want to subscribe to get notifications on it, you can subscribe to these as well. On the bottom left hand side of the thread you will see the link to subscribe

View threads in your subscription You can view a list of threads you are subscribed to at User CP -> Menu -> Miscellaneous -> Subscribed Threads. Or here

If your trying to obtain of list of interesting threads, ie. favorite threads. Use that instead.