A "breach" is an incident where a site's data has been illegally accessed by hackers and then released publicly. Review the types of data that were compromised (email addresses, passwords, credit cards etc.) and take appropriate action, such as changing passwords.

Final Fantasy Shrine: In September 2015, the Final Fantasy discussion forum known as FFShrine was breached and the data dumped publicly. Approximately 620k records were released containing email addresses, IP addresses and salted hashes of passwords.
Compromised data: Email addresses, Passwords, Usernames, Website activity
Good thing I changed my password when it was stated earlier...
Still... I have multiple email accounts and the one I use here... is merely one of them.