iCloud (more precisely, the iTunes in the Cloud feature) hosts your iTunes library. Anywhere you have service, you can download songs to your iPhone/iPod Touch/iPad. When you don't have a signal, you can still listen to whatever you've previously downloaded.
The rest of iCloud is basically an upgrade of the services offered in MobileMe, but for free. It synchs contacts, calendars, documents, apps and settings remotely. It also supports backups and software updates remotely, so that now it's feasible to have, say, an iPad for someone who doesn't have access to a computer.
So is it essentially identical (in this part) to the Google Music service. The first time you play a song it is streamed to your device and then recently played items are cached on the device along with any songs you select to keep on the device permanently?