Jack Dorsey: And they hired me a week later. And it was a dream come true, which is a weird dream for a kid.

Now the kid who ventured to New York when he was 19 has a new dream: to expand Square internationally, and start handling transactions in Europe and Asia. He's the new kid on the block again, and he will have some stiff competition.

Lara Logan: PayPal is a competitor of yours. It has a similar system. Google, Walmart and Target are developing their own systems. What prevents the competition from putting you out of business?

Jack Dorsey: Well, you know, our take on this is you can worry about the competition, you can constantly look in your rearview mirror and you can constantly look around and really not notice the road ahead of you. Or you can focus on what's ahead of you and drive, and drive fast, right? And drive within the speed limit, of course, but drive fast.

Lara Logan: But hopefully faster than everyone else.

Jack Dorsey: Faster than everyone else.

To keep his employees motivated and thinking, you won't be surprised to learn that Jack Dorsey is a bit unconventional. Instead of a company picnic or softball game, he took them to a place in San Francisco called Land's End. He wanted to make them think about the Golden Gate Bridge.

Lara Logan: Why?

Jack Dorsey: Why? Because we see the bridge as like this perfect intersection between art and engineering. It has pure utility, in that people commute on it every single day.

Dorsey's point to his colleagues is that when people look at the bridge, they don't think about the commuters or how it functions. They admire its simplicity and beauty. He thinks good software should work the same way.

Jack Dorsey: When people come to Twitter and they want to express something in the world, the technology fades away. It's them writing a simple message and them knowing that people are going to see it.

Lara Logan: And that, to you, is functionality and beauty.

Jack Dorsey: Yeah. It disappears. It disappears because it's so intuitive. It just works.

That's the thinking behind Jack Dorsey's latest invention, called Square Wallet, which radically changes the way we pay for things.

Lara Logan: Is this your favorite place to go for coffee?

Jack Dorsey: Yeah, it is one of my favorite places.

To show us how it works, Dorsey invited us to visit a cafe just around the corner from his office.

Jack Dorsey: What would you like?

Lara Logan: I will have a latte please.

Waitress: Is whole milk okay?

Lara Logan: No.

With the help of GPS, the barista's iPad knows Dorsey and his smart phone are in the house, and his face shows up on the tablet's screen before he even orders.

Lara Logan: So all your customers, I mean who have this app, they just appear.