They capture a second or two of (lower-resolution) video frames before and after the photo itself, plus audio. The UI on the iphone is that you hold your finger on the photo and it plays the "live" version. Under the hood IIRC it's just a short video + still bundled together in a container. The effect is reminiscent of the magical photos in the Harry Potter films, and when looking back at photos of one's kids from years prior it really is magical. To take them, the UI is the same as taking any other photo, except that you must know to keep the camera steady a second or two before and after taking the photo itself (it'll still be captured just fine regardless, but the "live" part will be a blurry mess if the camera's moving) which is the real genius of it—no extra effort, really, and it's automatic, provided live photos are enabled, so you don't have to decide whether you want to take a video versus a photo, you just take the photo and get a tiny little video to go with it.