A monitoring system regularly checks whether a server is up, how much disk space is left, whether a backup completed and whether a website is reachable. When something goes out of range, an administrator gets an alert.
This way many problems show up early — for example, a disk filling up or one RAID disk failing — and are fixed before work stops.
Example
A backup failed overnight — the administrator gets an alert in the morning and re-runs it the same day.