The product category will determine what items are displayed in the navigation bar on the left side of your shop.
The left box allows you to create a new category for that product, this will then add a button to your navigation bar with that category name.
The next box allows you to put this product into a category you have already used for another product.
In the above image you can see that the shop has at-least one product that has its category set as Book. When a customer clicks that link they will be taken to a page that shows all the products in that category.