You have a lot of email notification options that you can turn on and off whenever you wish through your Control Panel. You can have email notifications of replies to your messages, notifications of received PMs, Subscriptions to the various boards, etc.
All of these notifications are sent to the "hidden" email address that you have registered with your account. You can see what email address you have by checking your "Control Panel" and under the Main Configuration > Personal Information you can update both your "hidden" and "public" email address.
The subscriptions can be fairly large, so if you have a limit on the size of your mailbox then you should be careful in your choice of what boards you may want to subscribe to because if you do not read and delete the subscriptions then it is a real possibility that you will max out your available mailbox space in a short period of time.
In addition, you should make sure that you have a current email address so that you can receive these notifications.