The app previously had no way to enter a gift card at checkout, so the only available option was to use a credit or debit card. Following the update to version 3.4, users can tap "Buy with other payment options," which has a new section for entering a gift card.
Gift cards can be scanned with the camera on an iPhone or iPad or imported from the Passbook app, with the gift card total then applied to the order total.
What's New in Version 3.4The Apple Store app can be downloaded from the App Store for free. [Direct Link]
You can now make purchases with an Apple Store Gift Card. Use the built-in Camera to scan new Gift Cards or import existing Gift Cards from Passbook.