The notification center is a great tool for not only keeping track of messages but also new posts and replies in threads you may be subscribed to. Click on the link on the upper right, and it will display the last 5 notifications as well as a link to the page where you can see them all.

In the screen shot above, you'll notice that the stuff that's already been viewed has a white background, and the one that hasn't been viewed has a colored background. Click on the notification and it'll take you to the post in question, or if you simply hover over the item you'll see a checkbox on the right where you can mark the item as read.
Clicking on the 'See All' button takes you to the Notification Center in your User Control Panel....

If you want to change what kinds of things you're getting notified about, you can change that in the Board Preferences -> Notifications tab...

It's pretty self-explanatory. Check it if you want a notification by email or in the notification center, un-check it if you don't. Save your settings by clicking the Submit button (not in the screen shot, but at bottom right) and you're all set to go. Enjoy!