Host card emulation (HCE)
A technique that lets an ordinary app on the phone's main operating system impersonate a payment card to an NFC reader, with no secure element involved.
The first NFC wallets needed the card to sit in a secure element, usually on the SIM. That made mobile carriers the gatekeepers, and the US carriers building their own wallet duly kept Google Wallet off their SIMs. SimplyTapp showed in 2012 that the hardware could be bypassed, and Google built HCE into Android 4.4 KitKat in October 2013. Visa and Mastercard backed the approach in February 2014.
The catch is that the app has nowhere safe to keep long-lived keys. The fix was network tokens plus short-lived, limited-use keys fetched from a server and exhausted after a handful of payments, which the industry rebranded as "cloud-based payments". A stolen key is worth a few purchases at most, but the phone has to get online regularly to top up.