The model number is a complement to the serial number in most methods of product identification. Unlike the serial number, which is unique to each particular item, the model number is the same for all identical items. The term model 'number' is a often a misnomer as they are quite frequently alphanumeric, more often than serial numbers are.
Model numbers generally have a multi-part form, with each part signifying a different level of generality of the product. For example, the model number of my Sony Playstation is SCPH-9001, and that of its Dual Shock controller is SCPH-1200. The first part of the number is the same for both products, signifying that they are related. In contrast, the model number of my Sony NetMD Walkman is MZ-N505.
From an end-user point of view, the model number of a product is almost completely irrelevant. The main exception is when dealing with support or warranty issues, where the model number and serial number are used by the manufacturer's support division to identify your product and, often, to determine if it is still under warranty.