Notify on Stage Update is a per-Container feature where you can assign Users to be notified of changes to the contract's Workflow, but they do not need be involved in the actual Workflow process. Any Users assigned to this group will simply receive email notifications any time the Workflow is updated to a new Stage on that contract, whether it moves forward, back, or even skips Stages.
Assigning Users is as easy as clicking Notify on Stage Update above your Field Groups, and using the left right selector to assign your Users.
The email notification they receive will look similar to the one below. You can see when it was update, by whom, and the previous stage name and days in that stage. If the recipient is a User of UCM, they can use the link to access the Contract. (This feature is occasionally used so No-Login Users can be kept informed of certain Contracts without being involved or even a User of the system.)