CoffeeScript code is not processed by browsers that work with JavaScript code. Therefore to be executed, CoffeeScript code has to be translated into JavaScript.
This operation is referred to as transpilation and the tools that perform it are called transpilers.
To debug CoffeeScript in IntelliJ IDEA, you need source maps generated in addition to the JavaScript code.
Source maps
set correspondence between lines in your CoffeeScript code and in the generated JavaScript code,
otherwise your breakpoints will not be recognised and processed correctly.
JavaScript and source maps are generated by transpiling the CoffeeScript code manually using the File Watcher of the type CoffeeScript Source Map.
After that you can debug the output JavaScript code as if it were a Node.js application.
For more details about transpilation in IntelliJ IDEA, see the section Using File Watchers.
Debugging CoffeeScript is supported only in the local mode.
This means that IntelliJ IDEA itself starts the Node.js engine and the target application
according to a run configuration and gets full control over the session.
For more details about debugging Node.js applications, see Running and Debugging Node.Js.