Notifications are Photocase's message service. You can choose to subscribe to the comments made on photos, forum postings and News items. For example, if you choose, you can be notified every time someone comments on your new photo, or adds a new post to that forum thread about fisheye lenses.
To turn a notification on, simply look for the link on the bottom of the page that says "Notify me about new comments."
If you no longer wish to receive a particular notification, just click the link at the bottom of that notification and you will be unsubscribed from it.