Notification per user session is total number of notifications shown to the visitor. 

Live Conversion and Rating notifications have further activities e.g in case of rating notification, each review is counted as an activity/notification. Similarly, some notifications don't have any activities and are only displayed once e.g Visitor, Announcement, Coupon, Opt-in etc. You can view the activities for notification in the Activity Manager. So when setting up your notification/stream you should adjust Notifications Per User Session accordingly. 

Notifications Per User Session resets when the visitor closes his browser.