The 2D bar code (representing the 16-digit number on the associated magnetic card? [I blurred half of the numbers in the original photo]) is displayed, which can then be read by a special scanner in one of the 16 pilot stores in Seattle and Silicon Valley (which are listed in the app itself, and and on the Starbucks Card Mobile App web page

The main advantage over the magnetic striped card is that it allows you to see / check the balance without requiring a barista to print out a receipt.