CoCart works by connecting to your WooCommerce store via a series of API endpoints that specifically returns your customers session stored in the database either as a guest or a registered user on your WordPress site.
These sessions contain your customer’s shopping cart items, shipping requirements, discounts applied, tax’s and the totals of each item and the cart as a whole.
So no local storing in the browser is required to keep track of your customers information. All data is synced to your store. All you have to do is make a request.
With that data your then able to insert it into your designed UX/UI to display as you wish.
It’s pretty cool.