Yesterday a number of users of Apple's iCloud service found they could not access their e-mail. While Apple claimed to be working on the problem to have it fixed "ASAP," for affected users the problems are persisting for a second day.
On the iCloud System Status page, Apple notes the problem, claiming that for 1.1 percent of users the Mail service "may be slow or unavailable," and that if users are able to access their e-mail, it may be slow and show delays with incoming messages.
Being a problem with the central iCloud service, users may experience the delays or other problems on their Macs, iOS devices, and with Apple's Webmail interface on iCloud.com.
If you suspect your account is one of the affected ones, you can test this by sending yourself an e-mail either from your iCloud account or from another one, and if it takes longer than a few minutes to arrive, then it is likely your account is one of those affected by this problem.
Apple gives no indication on what the problem may be, and only mentions as it did yesterday that the services will be restored ASAP.