Understanding iOS Development certificates
app-store, certificate, code-signing, ios
Solution
Every certificate is just usual pair of private and public key. When you generate a new certificate, actually you save a private key on your machine, and send a part of public key to Apple. Then Apple generates a key by itself, and send you a public key as result (see Diffie–Hellman key exchange).
If you changed a machine and now don't have a private key on your new machine, Xcode is unable to sign your application with your certificate. Because you can only download a public key from the developer portal. So if you used "Automatic manage signing" Xcode took decision to recreate a certificate, because it couldn't find a private key. All this process is same for a Private team, and for iOS developer program. You can export your old certificate with private key from your old machine before you try to sign smth, so you don't need to revoke old certificate.
As for email, Apple just notifies you that your old certificate has been revoked, and it can't be used to sign apps now. Just like it written. It could been revoked because has been expired, or somebody else has revoked it (e.g. it was you). So to keep you informed, Apple sent you such email.
Problem
We received the email from Apple: Your iOS Development certificate has been revoked. There are answers on SO about how to restore your cert (1, 2) but I have some other questions - Why did it get revoked? What I did is try to run our app on my iPhone. I'm doing this for the second time - this time on a new MacBook to a new iPhone. Is this the issue that triggered the email? - What is the significance of this email? I can still run the app on the same iPhone. Uninstalled it and reinstalled it and it worked fine. Is there really an issue?