At some point after you have created an alert, an event on a story within the alert scope will cause it to trigger. When the alert is triggered, you are sent an email.
The alert log has a record of each time the alert was triggered.
How to view the log
To view the log for an alert, first open the alert page, then open the log panel.
You will see the most recent log records first. For each record, you can see the story which triggered the alert, the time, the trigger and the outcome.