When I get an e-mail I double-tap the home button, and touch the e-mail app. It's always running and I hear the new mail beep when it arrives. When I want to switch back to Safari or the Kindle reader I'm right where I was when I left and the apps don't have to restart... they're still running. Likewise when I'm listening to Tune-In radio it continues to run while I'm working / reading / browsing. The only time it pauses the internet radio is when I click a video link in Safari and a video starts. When I switch back to the radio I can pick up where I left off.
The iPad has always been able to multitask, but the APIs were not available to programers outside of Apple until recently. Thats why you could always download from iTunes or listen to your music in the iPod app when when doing other things. Third party apps have to be updated to use the recently opened APIs before they can perform background actions.