Two years ago, I met Square CEO Jack Dorsey at Third Rail, one of his favorite coffee shops in downtown New York. He held up a small plastic square and told me that the future of payments was in this tiny device.

The entire industry was about to change, he said.

Dorsey was in the middle of a major change himself. Recently ousted from Twitter, the company he cofounded, he rebounded by shifting his famously intense focus to a new pain point: the way we pay.

Square's pitch - a simple fee structure and technology that just works - was a quick hit with small merchants like Third Rail. Square now has 2 million users and an annual transaction volume approaching $6 billion.

That was just phase one, it turns out. Dorsey wasn't kidding about reinventing the entire concept of payments. Last week, he struck a partnership that will begin to bring his vision to the mass market.

This fall, Starbucks will begin accepting payments through Square's mobile app.

Read - Square's Starbucks vision: Magical cash-free payments

Or skip the line and perfect your pour-over method at home