Have you used a shopping cart?
If you go to the grocery store or to Walmart the first thing you do is get a shopping cart. As you traverse the store you put items you wish to purchase into the cart. When you have finished shopping you go to check-out. The web has an equivalent.
The Virtual Shopping Cart
On a website you may not need a physical basket in to which to put the items that you wish to purchase and you may not need wheels to roll it to the check-out counter, but you do need a way to keep track of the items that you wish to purchase. To shop on the web you use a software cart that is an analogy to the buggy that you roll around the brick and mortar store.
The software keeps track of the items that you select and can be recalled form the check-out page. You can change the quantity or remove items from the shopping cart before checkout. Sometimes you have to put an item in the cart to view the final selling price of the item.
If you have a website and want to offer more than a few items for sale you will need to provide a shopping cart. There are several free options that will probably be adequate for your needs if your volume is not too large. If you are operating a major eCommerce site you will probably need to go with a paid license cart to provide your customers with all the features they expect from a major online store.
Your hosting company probably has an option available if they are a full service hosting company. PayPal has an option available that can be used by anyone with a PayPal account. Most of the free options have a somewhat limited feature set. There is a comparison chart on Wikipedia that lists features and also has some pricing information for the paid carts.
There is also the option of outsourcing the whole process. There are companies that will host your catalog and provide a full service cart for your products and customers.
The little shopping cart icon in the corner of the page or near the product looks like a simple thing, but there is a major software program that clicking the link calls into action. There will be a database to hold the data. The payment page or the whole shopping cart needs to be on a secure server. That is the way that business is done on the Internet.