The USB ANT+ dongle allows your computer to receive the wireless signal from the speed sensor on your bicycle so that the Zwift app knows how fast you are going. That combined with the known resistance curve for the non-smart trainers that Zwift supports allows the app to estimate your power output.

MTA: They are available on Amazon for under $20. It doesn't have to be the Garmin brand. I have used the Suunto Movestick with a Garmin speed sensor.