Google Voice, which began as an app called GrandCentral before Google bought it back in 2007, is a difficult beast to explain. It's sort of like a phone management system--it gives users one number which, when called, rings however many devices that user wants (cellphones, landlines, work phones, whatever). It provides an alternate Web-based voice mail system which transcribes voice (sometimes well, sometimes with odd and hilarious mistakes) and pops the messages into your email for listening or reading. It's also a mobile app for Android and Web (that Web app can be used by the iPhone and Palm's WebOS phones) that can place outgoing calls.
Google and Apple had a bit of a scrap over Google Voice, which was rejected from the iPhone App Store for reasons that are still unclear. But despite that hiccup, and despite Voice's slightly confusing nature, it's achieved some pretty impressive popularity, with over a million users in about a year's time.
Google Voice was, up until today, an invite-only service, but Google now feels it's ready for mass consumption, and has released it publicly to all. Well, at least everyone in the U.S.--it's still America-only for now. You can try it out here.