CrunchGear notes that a version of the iPhone Push Notification Service API has been released to "a handful" of developers, and, according to them, will "surely" be released to everyone when iPhone OS 2.1 is released.
If you remember our WWDC keynote coverage (around 11:05 a.m.), the Push Notification Service maintains a connection with third party servers to alert you via an icon badge, custom sounds, or text alerts.
An app that uses this feature isn't really running in the background, but instead sort of registering itself with a metaphorical "hotel operator" that lives in your phone. Once there's something new to tell you, the hotel operator notifies you.
Hopefully this has little effect on battery life, but without actual, real-world use, it's hard to say.