Basically, it is a script that automatically adds a "cookie" to someone's browser when they visit your site. It can actually be used to add hundreds of cookies from different affiliates, so that if you visit someone's site, and then you go off to Amazon, Ebay or wherever, the original site's owner will get credit for directing you to the affiliate site, even though you never clicked on anything.
Most affiliates frown on cookie stuffing, if it's not stated as illegal in their TOS. I know that the EBAY Partner Network banned several hundred users recently for cookie stuffing.