Subscriptions are a way to keep track of different topics and/or forums. You can choose how you are notified about updates - for example by having them listed in your User Control Panel and receiving e-mail updates for each one.
Or if you don't want to manually subscribe to an topic you want to follow you can turn on the Option 'Notification for topics you've posted to, watched or marked as favorite' in the E-mail Notification Preferences Page inside the User CP.
How to watch a topic?
To subscribe to a topic, click the 'Options' link at the top of the list of posts then click 'Watch this topic'.
How to watch a forum?
To subscribe to a forum, click on the 'Watch Forum' link bellow the list of topics.
How do I manage my Subscriptions of Watched topics and forums?
You can see the List of 'Watched Forums' and 'Watched Topics' from the 'Email Notification Preferences' Page of your User Controp Panel. There you can select which subscriptions you wish to delete by Clicking on the Unwatch button.