Notifications let you know when different actions occur that affect your account. These actions could occur in your catalog or your network. Either way, you can control what you get notifications for and where you receive those.
Emails are sent to your account email address. Notifications display in the primary tool bar and can be marked as "read" when you're ready to dismiss them. All events from the past 90 days will appear in your activity feed.
Here are some links to all of the Notifications you can change the settings for when someone: