Airplay will stream content in iTunes from your Mac or PC to your Apple TV or Airport Express. You can go to your Mac and start playing something in iTunes, select the little Airplay icon and push it to your Apple TV or Airport Express. You can also use the Remote app on your iOS device to select the content in iTunes on your Mac and play it on your Apple TV or Airport Express. Note that if you have Home Sharing set up on your Apple TV you can do the same thing except you start at the Apple TV and pull the content from the Mac rather than start at the Mac and push it to Apple TV. Of course with Airplay, you don't need to have Home Sharing set up.
But the Mac/Apple TV integration is just one part of Airplay. The other part of Airplay is that it allows you to push content actually stored on an iOS device to your Apple TV or Airport Express. In this scenario, your Mac and iTunes are not needed at all and don't have to be on. All you need is your iOS device. To me this is the most revolutionary part of Airplay. I don't think it has ever been possible to have a mobile device in your hand with GB of content on it that you can make play on your TV and/or home theater wirelessly like this. All in HD and 5.1 surround sound. That is pretty cool. And streaming radio/music apps like Pandora are absolutely killer with Airplay used in this way.
When I visit the family for the Holidays, I'll be taking my Apple TV 2G and loading up a few Hollywood movies and home videos on my iPhone. When we get there, I should just be able to connect the Apple TV and Airplay the movies, home videos and photos, holiday music, and etc. on the big screen with no computer required.