Recovery Key?

Updated recently to two factor authentication. Going though all my accounts and updating due to recent fraud attempts. Apple says in case your account is hacked with two factor you need three things, a trusted device, your password, and your recovery key. In alarming terms they state if you don't have them you risk permanent loss of data.

So I don't recall getting a 'recovery key'. I read the help articles and was directed to sign in to apple ID site, go to security, then user "replace recovery key". That option doesn't exist. For the iphone it says go to settings, account, security, then tap "recovery key". Again, that option doesn't exist. So next I called apple support, and he but pointed me to the same places, but was as confused as I was and said I would be "good" as long as I have my device. But then I thought, what if its stolen?

So what is this recovery key? Apple won't give me one, but says they'll lock me out if I don't have it. Thanks.