American cheese, in the sense used in the United States, is a processed cheese, usually built on cheddar, Colby, or similar young cheeses. Emulsifying salts make it melt in an even sheet.
It is not a farmhouse wheel. Use it when the goal is a smooth melt. Use cheddar when the goal is the taste of cheddar. The category is wider than any one brand.
History
Melted cheese that stayed smooth was a factory problem before it was a flavor. In 1916 James L. Kraft patented a way to process cheese so it would keep and melt evenly. The method turned surplus cheddar and other young cheeses into a stable loaf that could be shipped across a large country. Deli counters and, later, wrapped slices made it ordinary.
The word American was already loose. It could mean a mild local cheese. After processed cheese became the everyday slice, the word settled on that product for most cooks. A deli may still slice a mild loaf and call it American. A package of singles may be process cheese, cheese food, or a cheese product, which are legal categories with different amounts of cheese and water. The kitchen treats them as one family because they melt in the same way.
How it is made
Young cheese is ground and heated with an emulsifying salt, such as sodium citrate. The salt keeps fat and protein from parting company. That is why a slice can melt over a burger without breaking into oil and strings. Color from annatto is common. The loaf is poured, cooled, and sliced, or it is cast as single slices.
This is manufacturing, not a cellar. There is no rind to wash and no age to wait for. The recipe can include more than one cheese, plus dairy ingredients, and the label tells you how far the product sits from straight cheese. None of those versions is a wheel of cheddar that was simply dyed orange. The orange cheddar myth is a different cheese.
Taste
The taste is mild, salty, and creamy, with a little tang from the cheeses underneath. It is not sharp. It should not be bitter. The texture of a cold slice is smooth and slightly rubbery, which is what lets it hold a square shape and then relax in the pan.
People who want the savor of aged cheese will find American cheese flat. That flatness is the design. It seasons a bite of beef or bread without competing. A sour, oily, or plasticky off-flavor is a stale product, not the style itself. A good slice smells faintly of cheese and salt.
In the kitchen
The right jobs are a cheeseburger, a grilled cheese sandwich, a diner cheese sauce, and eggs. The slice covers the food and stays glossy. Because it is already emulsified, it is also the easiest cheese to melt into a smooth sauce. Add a little liquid and keep the heat modest.
Do not put it on a cheese board, and do not grate it over a finished pasta in place of Parmesan. It will taste salty and soft, with none of the grain of a hard cheese. When a recipe wants cheddar flavor, American cheese will only give you the melt. Some cooks mix a slice into a cheddar sauce to keep the sauce from breaking. That is a technique, not a requirement.
Around the world
American cheese is a United States product, tied to the hamburger, the diner, and the home griddle. The processed slice traveled with those foods. Burger shops in many countries now use a similar square slice, sometimes under this name and sometimes under a local brand.
Other countries have their own processed cheeses, sold in triangles, slices, or tins. Those are relatives in method. They are not American cheese unless they are made in this style and sold as such. There is no protected region and no farmhouse original to seek out. Buy it for the melt. Buy a named cheddar, Jack, or Colby when you want a cheese with a place.