Apple has made iCloud live at iCloud.com. It obviously requires an Apple ID to access, but you also must have the iOS 5 update as well. That has not been rolled out to all just yet, but it comes today.
iCloud lets you store content in the cloud and access it across your various devices. It works with iPhone, iPad, iPod Touch, Mac, and PC. It's free with iOS 5.
With iCloud, MobileMe has been discontinued as a service. Contacts, Calendar and Mail services have been reworked to work with iCloud. Users can share calendars with friends and family, and they can get an @me.com push mail account (which doesn't have ads). Inboxes and mailboxes are kept up to date across devices.
App Store and iBookstore downloads and purchased iOS apps and books will be accessible across devices (not just the ones they're purchased on). The App Store and iBookstore also let you see your purchase history, and download apps/books to different devices by hitting the "iCloud" icon.
For more on iCloud and iOS 5 in general, read 114 Things You Should Know About Apple's New Offerings from the company's Worldwide Developers Conference, where this stuff was unveiled.
If you have a supported device, expect to get iOS 5 access today.
Now let's start worrying about iOS 6.