According to the Resource Center, "An alert notifies when a statistic enters a user-defined threshold or is no longer within a range of values. You can set an alert on any interaction type to notify a supervisor when an interaction go beyond a specific duration, when an agent transfers more than the average number of interactions, or many other metrics. "
It appears that you have to have the Supervisor role enabled to configure and receive alerts above and beyond SMS and email alerts.
I'm not sure about any sample scenarios.
You can read all about alert administration starting here: https://help.mypurecloud.com/articles/alerts/