In your toolbox in the upper right corner of the page, click on the Settings > Notifications link. Here you will be able to select when you wish to be updated on activity in the network.
You may, for example, wish to receive an email whenever you are mentioned in a discussion, or when you are invited to join a group. You may also wish to receive an email when things are posted to a group you belong to.
What email notifications you receive are always up to you. Of course, you can always log in to the network to see recent activity at any time.