Originally Posted by Robbie

Because the 1x1 pixel IS the actual site with your affiliate code in it. Not just a link to the site.

In other words the site in question (or sites in the case of "cookie stuffing") are fully loaded on a 1x1 pixel (which is too small for you to notice on the page). It's in an IFRAME
So it's the equivalent of the surfer actually visiting a bunch of sites...but they don't know they did.

Now they are effectively cookied for a multitude of sites. So if they go to any of those sites in the near future and spend money...then the "cookie stuffing" makes sure the bad guy gets paid.