Greylisting is a spam prevention method. When an email network "greylists" messages, they do not accept the initial incoming message, but rather instruct the sending mail server to try delivery again later (which most servers will do every few minutes). The assumption being that spam servers will not attempt to send the message again, but legitimate servers will.
A large percentage of spam is sent from compromised home and business computers. Spammers typically send messages from large numbers of these machines, but each machine sends only small batches of mail, in order to avoid detection, and they will almost never retry to send the mail when they receive the "try again" response that a greylisting server sends.
Greylisting is a very effective anti-spam tool (our tests show a decrease in spam of 80% to 90% when greylisting is implemented), but it can cause delivery delays. Those delays will vary, depending on the sending server, but are typically no more than a few minutes. Only the mail servers exchange the "try again" message. It is not passed along to the sender or recipient.