The "Korean thumb" is the Korean version of "the finger". What you do is make a fist and then insert your thumb between your index and middle finger. To the person on the business end of the Korean thumb, it looks like some kind of emerging sex organ. I believe it's symbolic of an emerging clitoris. All in all, it means "fuck you!". Ostensibly if you insert the thumb between the middle and ring finger, this is far worse. It means "fuck you in the ass!"

Oddly enough, in America, this gesture is not rude. Many times you'll play with a small child and go "I got your nose!" and shove your thumb between your fingers. So, word of warning, if you're on a subway in Seoul and you're trying to entertain some curious child sitting next to you, don't play that game with him. His mother will beat you senseless if she sees you.

Side note: This gesture is considered rude in many places in Asia (like Japan) as well, as some users inform me, in many places in Europe.