There are two options for email notifications that WordPress MultiManager can send:
Email notifications for a disconnected site - This option allows you to choose if the system should send you emails if the site gets disconnected.
Email notifications for available updates - This option allows you to choose if the system should send you emails if there are available updates for the WordPress core or any of the plugins or themes of the site.
The notifications are sent to the contact addresses for your account defined in the My Account section.
Each option can be defined globally for all sites via the WordPress MultiManager > Email Notifications section, as well as on a per-site basis via the WordPress MultiManager > WordPress Sites section > Manage button for each site.