As a product is added to your store - whether manually or via CSV import - it is written to the store's database. The identification for the product (as it appears in the database) is called the "Catalog ID." It is the unique identifier used by the database to reference the product.
The Catalog ID can be seen when viewing a specific product in your Shift4Shop Online Store Manager. As you're viewing the product in the admin, look at its "Information" tab, and you will see the Catalog ID just above the ID/SKU. You can also see Catalog IDs when you export the product information via CSV file. It will be the first column of the product export CSV file, and it will be labeled as "catalogid."
Catalog IDs will be used by the store software for just about everything related to the product, including URLs, Order Item listings, inventory tracking, promotion manager functions, and anywhere else the products are referenced. It is also important to note that catalog IDs are created and assigned specifically by the store's database.
Since the Catalog ID is the main identification for the product on the database, it cannot be edited or altered. When you delete a product from your store, you're essentially deleting the Catalog ID, and it will never be used by the store again.