Users can sign up for alerts from the Activity Stream, comments, as well as comments on gradebook or dropbox assignments! Your teachers, parents, and students can use this via the blue "Alerts" button.
Only posts specifically entered into the Activity Stream will generate alerts, as opposed to notifications from other sections of the group space, which will appear on the Activity Stream but not generate a true alert to subscribed users.
Parents can sign up for activity stream alerts from their main dashboard and be automatically subscribed to all activity stream updates for their children and groups. Parents also have the option to go into each child's groups and sign up for only the individual group's alerts, if they prefer.
If you are interested in enabling Activity Stream alerts in your LMS, please have the administrator of your site submit a support ticket.
Here is a quick video of how to sign up for these alerts as a user.