As CoolHunting wrote in July (without knowing about Dorsey's involvement):
The innovation is in a small, plastic card reader that fits in to the headphone jack of an iPhone (or iPod Touch) and transfers the credit card's swipe data to the app. After the employee enters the amount to charge, the customer confirms by scrawling their signature with their finger and then either one enters the customer's email address to send the receipt to. The payment is processed by Square for a small percentage plus a fixed fee; the funds are transferred directly to the store's bank account, cutting both time and complexity on the processing side. The customer's receipt includes a map showing the location of the transaction which is handy for those who record, sort and file such things.