As expected, when iCloud comes out this Autumn, it will replace MobileMe, and includes the basic MobileMe services of syncing calendars, contacts, and mail.
Documents in the cloud: When you work on, say, a Pages file, you can save the document to the iCloud service. Any devices you own that have Pages on them will have access to that saved file; the same is true for other applications and documents. iCloud is OS agnostic; it will work with iOS, OS X, and Windows.
Photo Stream: Photo Stream lets you push images to iCloud, and make them available to all of your devices. Photo Stream is intended as temporary storage, however; images will be purged after 30 days. Photo Stream will be very useful for vacations and business travel. You can upload images to Photo Stream as you go, freeing up space to capture more images, and have them all waiting for you when you get home. (Unless your trip lasts longer than 30 days, of course.)
iTunes in the cloud: As expected, iCloud offers the ability to sync your iTunes music library with all of your devices. You can now download any music you purchased from iTunes to up to nine Mac or iOS devices. If you purchase a new song on your Mac, and you want to hear it while you're off traveling with your iPad, it will be available for you to download.
Tunes Match: Even better, iCloud includes a feature called Tunes Match. If you've ripped your own music to iTunes, Tunes Match will scan your iTunes Library and see if those songs are also available from the iTunes Store. If they are, iTunes will place a copy of them in your iCloud service. Tunes Match will be an add-on subscription service.
With the exception of Tunes Match, iCloud is free, with a few restrictions: mail, documents, and backup are limited to 5 GB of storage. That storage space doesn't include iTunes music, books, or apps you've purchased, or photos stored in the Photo Stream service.