System notification are used to communicate to guests when something has been changed/updated in their loyalty account. When reviewing a guest's timeline, you will see many system notifications listed in purple.
The messaging in these notifications can be updated through the Notification Templates section of the dashboard. To find out which notification template the messaging is coming from, view the right corner of the notification.
Notification Templates are found in the dashboard under Settings > Notification Templates. The image above is displaying messaging from the "Pending Checkin" notification template.