Here's how Amazon explains the process on the Amazon Go FAQ page:
"Our checkout-free shopping experience is made possible by the same types of technologies used in self-driving cars: computer vision, sensor fusion, and deep learning. Our Just Walk Out technology automatically detects when products are taken from or returned to the shelves and keeps track of them in a virtual cart. When you’re done shopping, you can just leave the store. Shortly after, we’ll charge your Amazon account and send you a receipt."
Basically, Amazon wants to make grocery shopping suck less by cutting out the part you hate the most. Imagine never having to worry about understaffed checkout lanes, or self-checkout kiosks that never work, or all those strategically placed impulse-purchase items you fall for every damn time. It's worth pointing out, however, that the tech-heavy concept looks ripe for erroneous charges and potentially alienating people who don't own smartphones, although that remains to be seen.