Processed cheese is staple food product with excellent keeping qualities and a smooth creamy texture. It's also known as process cheese, pasteurized process cheese, cheese food, and various permutations thereof.
Processed cheese is made of a blend of natural cheeses chopped up into tiny bits; the particular mixture of natural cheeses will determine the flavour of the end product. Water is then added to the mixture, sometimes along with milk solids and other flavourings like ham or onion. Then emulsifying salts (such as phosphates or sulphates) are added; these ensure that the fats in cheese will not separate when the product is heated, as happens with natural cheese. Then the mixture is pasteurized, killing any living organisms which would cause the cheese to mature or further develop in flavour. Finally, the whole mess is melted and mixed together to make a homogeneous emulsion which can be extruded into sheets (American cheese), poured into block molds (velveeta), or, with extra water added, packed into jars as a sauce (Cheez Whiz).
Although I find processed cheese bland and rubbery, it is prized by commercial cheese users (fast food restaurants and the like) for its smooth texture, stability when heated, and long shelf life. If you want to make your own processed cheese, there's step-by-step instructions at class.fst.ohio-state.edu/FST401/401%20product/Process-Product/Cheese/processed_cheese.htm. I'm sticking with natural cheddar, though.