The iCloud.com domain name was owned by Linkoping, Sweden-based desktop-as-a-service company Xcerion, which provides a storage-as-a-cloud service. Xcerion's iCloud service was recently rebranded to CloudMe, and the company acquired the CloudMe.com domain on April 5, 2011. The rumor goes that Apple was responsible for Xcerion's rebranding efforts, though neither company has confirmed this. In fact, a Whois lookup still shows Xcerion as the owner of the iCloud.com domain, navigating to iCloud.com redirects to CloudMe.com, and Xcerion currently owns the iCloud trademark.
Although Apple has not announced a cloud-based service, the general consensus (fueled by rumors and speculation as always) is that Cupertino is interested in competing with Amazon's recently announced Cloud Drive. The difference is that Apple wants the music industry to be onboard as well (Amazon started its service without getting approval from the big record labels). Cupertino has reportedly already procured deals from at least two of the big four labels (Universal Music Group, Sony Music Entertainment, Warner Music Group, and EMI Music) within the last two months, according to All Things Digital.
Apple will reportedly let users store songs they've purchased from its iTunes store, as well as other songs stored on their hard drives, and listen to them on multiple (iOS?) devices. Amazon's service does the same thing, but if Apple gets approval from the music industry it will have one advantage: store a single master copy of a song on its servers, and share that with multiple users. Amazon's service meanwhile requires users to upload a copy of every song they want to access remotely.
Amazon offers its users 5GB of storage for free, which is upgradeable to 20GB with the purchase of any Amazon MP3 album or from 20GB up to 1TB at $1 per gigabyte. It's not yet clear if Apple intends to charge its users for iCloud, or whatever it ends up being called (the term cloud in regards to computers really isn't that mainstream), or if it will absorb the storage and licensing costs on its own. A rumor from earlier this month suggested that Apple recently ordered 12 petabytes of storage to support not only a music cloud, but a video one too.