Apps don't go in Passbook, but passes do. You can get passes via both the Starbucks and Apple Store apps. If you sign up for an account in the Starbucks app, you can create a pass and add value to it (or enter an existing Starbucks gift card number). The Apple Store app allows you to send gift cards to people, which can then be added to Passbook.
Check out http://support.apple.com/kb/HT5483 for more info.