Copyright law and "Fair Use"

I’ve seen the term “fair use” used on this board, and I’m hoping to get an exact clairification. I know that since this message board is owned by the Chicago Reader newspaper, the issue of copyright violations is taken very seriously here. Can anyone tell me what exactly does “fair use” mean under copyright law, and what it entails?

This is a nice essay:
http://www.templetons.com/brad/copymyths.html

This is a website devoted to copyright and fair use:

Fair use is ultimately determined by the following guidelines:

Unfortunately, in the real world, the only precise meaning of “fair use” is “that part of the copyright law that causes people to tear their hair out trying to come up with a precise meaning.”