How can CapitalOne on iOS read my credit card? I was using the CapitalOne app and got asked to verify my identity as an added step before being shown my full credit card number, but today I got offered a new verification option: Tap one of my other cards against my phone to verify my identity. 

I followed the instructions and sure enough, all I had to do was tap my card and my identity was verified. Is this based on a new iOS capability, and how does it work?
The Capital One credit card has NFC capability, and similarly modern iPhones have NFC capabilities. This is how the phone and card communicates with eachother.

App developers can use NFC through Apple's "Core NFC" framework, which has been available for developers since iOS 11. So that's not really "new".

iPhone 6 and newer have NFC chips, but you'll need an iPhone 7 or newer for apps to be able to use NFC through the Core NFC framework.