CoffeeScript is a language that compiles to JavaScript . Its compilation generates a readable and pretty-printed output. The goal of the language is to simplify the JavaScript language, by defining syntactic sugars that enable you to write CoffeeScript code that is shorter and more readable than its JavaScript code equivalent. You can use the language in any type of application in which you would use JavaScript: game developpement, interactive websites ... etc.
There are 2 major versions of the language right now: CoffeeScript 1 and CoffeeScript 2. The second one compiles to a modern JavaScript code version that may not be supported in all browsers. In that case, you may want to transpile the generated modern code into an older version of JavaScript. To achieve this, you will have to install a transpiler like Babel.