Square’s first product, Square Register, allows registered members to accept debit and credit card payments on mobile devices by using the Square Reader, a small card-swipe dongle that plugs into the device's audio jack. Essentially, the Square Reader, which is provided for free, can turn an iPhone, iPad or Android mobile phone into a point of sale terminal.
Square followed this up with a product called Square Wallet. It's a digital wallet app that links the member's credit card information, loyalty cards and available gift cards to a Square account, allowing the member to pay for purchases wirelessly from vendors belonging to the Square Directory.
This iPilot1 tutorial demo's the Square Register app user interface on an iPad.