I think the two easiest answers to this question are "convenience" and "context awareness".
Smart devices are incredibly convenient, they are already on our persons much of the time, they are often Internet-connected by default, and they are ready to use which just a tap. No more fumbling around to find a PC or pull out a laptop. That said, this still doesn't differentiate an app from a website. Apps however have presence on the device itself, not only within the browser. Thus they are also available at just a tap (no more URLs) and can store identifying data (single log in on app launch). This compounds this convenience, making the shopping experience as seamless as possible.
However the more interesting advantage smart devices present is their context awareness. They come bundled with an array of sensors most traditional devices do not have. GPS, camera, accelerometer, proximity sensors, NFC, etc.. Leveraging these sensors can create a richer and more rewarding experience.
I can photograph a physical product to see competing offers from other stores, use the GPS to find these stores near me and navigate to them, and finally use NFC to swipe my store loyalty "card". Using an online-only example, I could set up an automatic reminder on an item, to notify me when it comes back in stock or when its price changes. Many of these features are slowly being replicated on the web, but once again, smart devices present a more convenient packaging for the same functionality.