It's basically just storage space out there on the internet somewhere...
So, for example, if you buy something on your iPad then it becomes available pretty seamlessly (alledgedly, I've not actually tried it) on your iPhone.
You can also back up your contacts and calenders to iCloud, so without needing to plug in an sync your contacts and calenders would then match on both of your devices. Add something on one and it appears on the other.
And the if your computer supports iCloud the same happens on there too.
If you've got an iCloud enabled application, Pages for example is meant to do this, then you can work on your iPhone on something and then pick up your iPad and it will see exactly the same document.
There's lots of Apple fluff about it here:
www.apple.com/icloud/
In the end it's nothing that you couldn't do with some careful syncing with your computer. But now you can do it without plugging things in in a careful order and syncing in sequence. And this is now heading towards a time when you no longer need a computer to use an iOS device at all, and how many people end up using their computer just to backup their iPad?
As is typical with Apple technology they don't actually invent anything new, they just make it all easier to use.