The Shopping Cart is a way to note down items you are interested in purchasing.
As you find domains you wish to purchase, press the "Add to Cart" button. When you do this you are adding the item to a list of items you are interested in before proceeding to the checkout.
When you are finished, review your shopping list by pressing the cart icon at the top of the page. When your cart contents are shown you have the option to re-check the availability of the domain names and remove items you are no longer interested in.