Adding to the answer above.
- Generally if you're playing a video on your iPod Touch (or iPhone or iPad), you can tap an Airplay button (if there's an AppleTV on the same network), select the AppleTV from a list and the video will 'pause' on the iPod and start playing on your TV.
- If Airplay is selected as the output 'device', it can lead to interesting side - effects. I launched a game the other day and music started blaring from my surround sound system. I didn't realise it was possible to play a game on an iOS device but have all the audio coming from the AppleTV / sound system.
- If you select Airplay Mirroring, then you can view whatever's on your screen, but at a relatively low resolution and with big black borders around it. Almost anything you view on your iPod can be seen on the TV.
- If you have Airplay Mirroring selected, and launch an app which natively supports it, they can display whatever they like on the TV. So some games put a dashboard on the iOS screen and the race screen on TV. Or Netflix plays the video on the TV screen and has the controls on the iOS screen.
- Finally, Airplay playback can be disabled for some sites. I don't know if it's still disabled if you turn on Airplay Mirroring - I've heard it's true but I haven't experienced it myself.
Hope that didn't confuse things too much.