Anomalies can happen in any system. Technically, you can always find a never-seen-before event that could not be found in the system's historical data. The implications of detecting those observations in some contexts can have a great impact (positive and negative).
In the field of law enforcement, anomaly detection could be used to reveal criminal activities (supposing you are in an area where the average person is honest enough to identify criminals standing out of the distribution).
In a network system, anomaly detection can help at finding external intrusions or suspicious activities of users, for instance, an employee who is accidentally or intentionally leaking large amounts of data outside the company intranet. Or maybe a hacker opening connections on non-common ports and/or protocols. In the specific case of Internet security, anomaly detection could be used for stopping new malware from spreading out by simply looking at spikes of visitors...
