An open relay is a SMTP server that allows users outside the local domain to send mail to users at another non-local domain. Spammers use many open relays to make their origins difficult to trace.
SMTP Servers and Open Relays - newsletter article from the A3C Connection provided by the Academic Computing and Communications Center within the University of Illinois at Chicago.
abuse.net mail relay test - an experimental mail relay testing service provided by the Network Abuse Clearinghouse.