Send me stuff
When you press the button on the front of the Dash Button, a number of things happen inside it. First, the button press wakes it from a deep sleep, which is how the Dash Button can run for months from the small AA battery. Next, the device blinks the LED white to let you know you have pressed the button, and connects to the Internet over your Wi-Fi connection. Then, the fun bit happens: It orders the product from Amazon by sending a simple message to Amazon, the same way that you fill out information on a website and press "send". All that this message contains is the unique serial number and a few bits of diagnostic information, such as the Wi-Fi signal strength and the battery life.
That might sound like a bit of an anticlimax, but that's the trick of the Dash Button: It's a very simple computer dedicated to performing this one task. This is the clever bit, though, because part of the information that this message contains is the unique serial number assigned to the Dash Button when it was manufactured. This identifies the individual Dash Button, which Amazon has associated with your Amazon account and the specific product that the button buys. So, when you press the button and Amazon receives the short message, they know that you have pressed the button and want to order more potato chips. If you have multiple Dash Buttons, each one has a different serial number that is associated with a different product.
Once the message has been sent, Amazon sends a response that acknowledges the request, and the Dash Button changes the color of the LED to green, then dozes off again after a few seconds to save battery power. Amazon claims that the AA battery included in each Dash Button should be good for at least a thousand button presses.
There are also a few failsafes: You get an alert from the Amazon app that allows you to cancel the order for up to a half hour after the button is pressed, and you can't order each product more than once every 24 hours.