If you follow an app item (e.g. a bug), you will be notified about activities happening on it e.g. when someone adds a comment or when someone attaches a file. The notifications will be through email as well as through the notificiation center. If you are an assignee, project manager, or a state manager, then you are automatically notified and there is no need to explicitly follow the task.
To unfollow, simply click on the Unfollow link on the item's Overview tab on in the footer of the email notification.