The app is Brushes [App Store] and it allows painting on the iPhone /iPod touch screen using your fingers and a variety of brush styles. If you have a Mac, you can export your work at resolutions up to 1920x2880. The app also saves a record of your brushstrokes and other actions and can replay them on your Mac. The artist who did the New Yorker cover, Jorge Colombo, obviously has impressive talent. You can see some of his other iPhone work here.
Colombo told the New York Times he loves the app because it "made it easy for me to sketch without having to carry all my pens and brushes and notepads with me, and I like the fact that I am drawing with a set of tools that anybody can have easily in their pocket."
This video will show you a stroke by stroke look at how the cover was created.
If you're looking for more info on this app try the developer site here. Another similar app at the same price is Colors, [App Store] which has also been responsible for some impressive artwork.
Wow. Just wow.