A 'complaint' is something the subscriber sends to their ISP in the form of marking your email as spam. This is usually done by clicking the 'mark as spam' button within their email client. With most ISPs, this action sends a message to our server and registers it as a 'complaint'.
Through Email System, the addresses are automatically unsubscribed. This prevents them from ever receiving another email.
Garnering many complaints or bombarding an unsubscribed address can get you blacklisted by ISPs.
The complaint meter is mainly used for this purpose: to unsubscribe those addresses that may not want or care to open the email or click on the unsubscribe link to opt out. Again, you don't necessarily have to do anything, but a lot of complaints may mean you have to change your subject lines or content to be more recognizable to subscribers, or even reevaluate the validity of your list.
A complaint is registered only from certain ISPs who send errors to Email System. Not all ISPs do this.
ISPs generally consider it a problem if 1 address out of 1000 complains to them.
You are able to view the email addresses that complained, but not the reason for the complaint.
In summary, a 'complaint' is reported when the subscriber marks your email as SPAM within their email client; a literal complaint is not registered.