Let's say for some reason Apple shuts down your Apple ID. Usually this is because of repeated attempts to sign in with the right Apple ID (usually your Apple e-mail address) but a wrong password. (More on this below.)
Apple sends you an e-mail with a link to reset your password. But it is sent to your Apple e-mail address. Which no longer functions.
So there's a "rescue" e-mail address you should always have set up that's different from your Apple e-mail.
Because there's a section in Manage my Apple ID that allows you to enter alternate e-mail addresses, there's some confusion. I answered this question on Macintouch a day or so back, and here's another answer to a wrong assumption:
M Young wrote,
"Only you can't add a rescue email address directly from the My Apple ID site."
The Rescue email address is not added from the option to add email addresses, but from the option below "Password and security." That is where, after answering security questions, you'll be able to add or change the Rescue email address.
Once we had our Apple ID shut down by Apple. After a lot of troubleshooting, I found that one of the four or five devices accessing that Apple ID had been left with an outdated password. Every time it tried to sign in, it generated one more wrong-password warning.
So make sure if you change your Apple ID password that you carefully change it on any device that might sign in.