When the image first appears, count how many men there are, then wait a couple of seconds. After the top halves swap positions, count them again. The first time you should count 12; the second time, 13.
( Wait! The image is about to change. )
There are (IMO) two reasons this is so hard to wrap your mind around. The first is that the drawings look unrefined, which disguises the fact that the solution is very subtle, giving the viewer few key features to use for reference. About the only clearly identifiable body parts are heads, torsos, arms, legs, crotches, and feet. Note that their hands are all hidden behind their backs — crafty!
The second reason this illusion tends to defy analysis, I think, is because there is no "smoking gun" solution to it, something you can point to and say "Aha! Here's where the 13th man comes from." That's because the 13th man comes from all 12 of the others. Yep. Don't see it?
Want to appreciate
exactly what's happening
to the animated image above
and to your eyes? Click here.