In modern usage, it applies to all arguments, not just on the internet. The law says that, in any argument, the first side to compare his opponent to Hitler or the Nazis is automatically deemed to have lost the argument. That is, saying something like "You're just like Hitler." automatically disqualifies one. It doesn't matter what the topic is—politics, psychology, chemistry, economics, etiquette, flower arranging, whatever—a comparison to Hitler immediately loses the argument.
The rationale for this seems to be that Hitler was a uniquely evil person (though there are people and groups in the modern world that seem to be vying for that title), so that any comparison between him and anyone else is unspeakably tasteless.
There is another Hitler-related principle that is actually an instance of the Association fallacy, involving things like "Hitler was a vegetarian", or "Hitler liked dogs". This is just used to confuse the issue. Some people sometimes try to use literally any belief or lifestyle choice shared by Hitler as proof that it is evil. Such arguments are transparently stupid. Sometimes people mix in a bit of the No true Scotsman fallacy, saying things like "Well, Hitler wasn't really a vegetarian." This is even more stupid.
Godwin's Law is merely an observational rule and is not meant to comment on conversations that happen to discuss Nazism. For example, Godwin's law does not apply to discussion of connections between Darwinism and Nazi policies on eugenics. Note, however, that Darwinian evolution was about natural selection, while eugenics was about artifical selection. Eugenics, with its intentional manipulation of human reproduction through forced sterilization, is generally considered evil. The extinction of trilobites is not.
Other Laws of Internet Arguments:
- How to post about Nazis and get away with it - the Godwin's Law FAQ
- George Soros Compares President Bush to Nazis - an example of Godwin's law
- Hitler Ate Sugar - a nice explanation of the Association fallacy
- Article by Mike Godwin, with the law formulated there. The Washington Post