The feature is called FaceTime Audio. And no, you do not need to make a video call to use it. It's strictly an audio-only call. The quality of the call is made possible by VoIP...Voice over Internet Protocol. It's a telephone call made over the Internet instead of the public switched cellular networks.
Here's how you use it. Go into your contacts list and pull up the name of the person you want to call. In the example from the photo above, that's our buddy Lauren. If you scroll down about 2/3 of the way on her contact page, you see an option called FaceTime. To the right are two icons. The camera icon let's you make a FaceTime video call, while the phone icon lets you make a FaceTime audio call.
Press the phone icon next to FaceTime and in no time at all, you will experience the highest quality phone conversation you have ever heard. It's almost surreal. Once you do this, you will likely never use cellular as your primary calling method. And there's an added bonus. If you make the call when connected to WiFi, the calls do not count against your bucket of data. FaceTime audio! Winner, winner, chicken dinner.