Users discover details
While the issue clearly isn't affecting all iCloud users -- or even most, it appears -- it's generated a number of lengthy discussions on Apple's Support Communities forums. User Grant Grueninger has provided perhaps the best summary, including some more details about what's going on behind the scenes.
As explained in that forum post, if you're having issues with iCloud data syncing, you'll want to check a particular log file in your user folder on your Mac to see if your sync issues are due to this problem. (The following assumes your Mac is logged in to the same iCloud account as the Macs and iOS devices having iCloud-data-sync issues.):
Open the Console utility (in /Applications/Utilities).
In the file list on the left, find ~/Library/Logs; click the arrow next to it to view the list of log files.
Scroll down to locate a folder called Ubiquity; click the arrow next to it to view its contents.
Under Ubiquity, find your username; click its arrow to view its files.
Under your username, locate the file named ubiquity-digest.log (with no number after digest); click it to view its contents in the main Console window.
Scroll to the bottom of the text.
If you see the following two lines, over and over (with different timestamps, of course), your account is likely among those affected:
[13/09/25 10:04:32.146] there was a http error 503 while talking to iCloud reason: ubiquity account locked
[13/09/25 12:04:32.509] disconnected from 'iCloud'
If you scroll up and locate the first instance of this error, you can determine exactly when the problem started for you. (Mine started at 11:51pm on 9/18/2013, and my log file currently shows roughly 4,000 such errors.)
If you don't sync any app data with iCloud on your Mac, you can instead check your iCloud account on your iOS device, though you won't see the same level of specificity:
Open the Settings app.
Tap the iCloud item.
Scroll down and tap Storage & Backup.
Tap Manage Storage.
Scroll down to the bottom of the screen.
Normally, any apps that use iCloud to store or sync data are listed here, along with how much space their data is currently using. However, affected users will see only device backups and Mail.
While this issue has been frustrating for users, it's also been challenging for developers who rely on iCloud for storing and syncing their users' data. Because the issue happened so close to the release of iOS 7 and new iPhone models; because there's no easy way for a developer to determine if a particular user's iCloud account simply isn't syncing; and because many users aren't having problems, it's been difficult for developers to troubleshoot user reports -- or even to realize that this is a wider, iCloud problem, rather than random sync issues.