The App is called Everyday Looper and it lets you grabs a short snippet of audio recording and loop it, playing it back over and over again. You can then add another bit of audio to it, and the idea is to eventually end up with something resembling a song.
The app has a fairly steep learning curve, apparently mainly touch/swipe controls that take time to adjust to. That said, once you’re up and running, with a bit of luck, you might end up with something half as cool as the video below. You’re also likely to find yourself humming as you click your way through to find the $5 app in the appstore.