While Apple doesn't allow 3rd party apps to run in the background on the iPhone or iPod touch,* Silicon Alley Insider notes that you can listen to audio in Mobile Safari while using other applications. It's this trick that MLB exploited with At Bat 2010. With the tap of a button, At Bat will push an audio stream to Mobile Safari.
Note that MLB didn't come up with this trick, nor is their app the first to exploit it. ESPN Radio does it, as well as Scanner911 and FlyCast. Still, it's nice that MLB's devs acknowledged that some users might want to check email or hop onto Twitter while listening to game, and made it easy to do so.
Now if only Pandora would follow suit.
*Yes, you can enjoy the benefits of background apps with a jailbroken iPhone, but that's a different post entirely.