Chile con Queso is a “Mexican” cheese sauce with chiles in it, used as a dip or as a sauce over dishes such as enchiladas and burritos.
The sauce is not really Mexican; it is actually more Tex-Mex. Some writers speculate that the inspiration for it may have been asadero cheese, roasted chiles and chorizo sausage pan roasted together over a fire.
For the cheese, some North American versions use cheddar, Longhorn or Monterey Jack; some use processed cheese, and also add a meat such as cooked ground beef or crumbled cooked sausage. Some recipes add cream. Diced cooked tomatoes and sautéed onion are used. The chiles are usually canned or bottle jalapenos.
Many crockpot recipes exist for Chile con Queso. The sauce is usually kept hot, either in a crockpot or in a chafing dish. When cool, it will congeal.
Chile con Queso is often served at ballparks with tortilla chips, and as a starter at Mexican restaurants in North America.
You can also buy it ready made in jars. Some commercial versions are often day-glow orange.
In Mexico, they do make melted cheese in a bowl (queso fundido) melted in an oven or on a grill, on its own or with things such as sausage and mushrooms added, but it is pure cheese, not a sauce, and has the consistency of a raclette or melted cheese.