enable peer-to-peer and merchant credit card transactions in the real world far beyond what’s capable today in most countries.

What you get is a small dongle (which I can only assume is the “Square”) and the scanning application to process the transaction.

The idea is if you are a Square merchant and someone wishes to purchase a product or service from you, all they need is a debit or credit card, a finger (to sign for the purchase on the touchscreen phone) and an email address to receive the receipt. From the article on Wired:

Square is targeted partially at small business owners who don’t want to sign up for full-scale credit card merchant accounts through the usual venues. One perk for them: a built-in loyalty program, so that customers don’t need to remember to bring along their stampable card in order to receive a free eleventh coffee, sandwich, bottle of wine, and so on.

Signing for a purchase using Square

The Square receipt