Software in a mail server that delivers messages to recipients. When you get a
MAILER-DAEMON@whatevercompany.com message in your inbox, the server at that company is informing you that it is returning your message because of some failure. The "to" email address may no longer be valid, or there may be a problem routing the message to the appropriate mail server. Your domain name may be on a blacklist, and the server is refusing all incoming messages from it. See
blacklist.
Chances are also good that you never sent the message in the first place. Your email address could have easily been copied by a worm from someone else's address book and used as a "from" address without your knowledge. See
daemon and
email virus.