At Admin Panel -> Settings -> Switches, the "reporting of topics and posts" switch enables a system whereby people can click a report button to tell the site administrator that there's a problem. This can help you discover problems much faster than you'd notice them on your own.

When the switch is enabled, you can configure where the report goes at Admin Panel -> Settings -> General -> "Reports". You can select to send the reports to all admins, the original admin, admins plus moderators, et cetera. You can also configure the standard types of problems people can select from.

A reports page will appear in the moderator control panel, topic resolved and unresolved reports. This is where moderators will collaborate and can mark any resolutions that aren't automatically recorded (such as "no action" resolutions where the report doesn't warrant action). The resolution of a report is communicated automatically to the reporter.

See report variables for the nuts and bolts of how you can customize report notifications.