Run "mailq" as root to get a better overview of the contents of the /var/spool/mqueue directory. Also check the postmaster notifications in the local mail inbox of the root user, i.e. /var/mail/root file.
If the output includes messages that are sent from outside your organization to destinations outside your organization, your mail server is probably an open relay that is being abused by spammers. This is a serious configuration error and other mail server administrators may hate you for it.
If the system is your main mail server, it should accept mail in two categories:
from inside your organization to any destinations
from outside your organization to destinations within your organization only
You should never allow a mail server to accept mail from anywhere for delivery to anywhere: such a configuration will be abused by spammers eventually.
If the system is not (one of) your main mail server(s), its port 25 should not be accessible from the Internet at all, and it should normally be configured to deliver all outgoing mail to your main mail server(s) only. The main mail server(s) would use their configuration rules to determine if the message can be forwarded to its actual destination or not.
If the mailq output includes only bounce messages for mails that clearly are not sent by you, a spammer has used your domain name as a fake source address in a spam campaign, and you are getting the error messages as backscatter. If this system is one of your main mail servers, there is not much you can do to completely block this, but there may be some ways to limit the flood. If this system is not used as an actual mail server, just block access from Internet to port 25.
If the messages in your mail queue are bounce messages for mails that are actually sent by your system, you may have a malfunctioning e-mail generator software that is sending messages to invalid destinations. Look at the bounce messages to identify the origin of the failed messages, find the e-mail generator and fix it.
