What is the scope of app.js in node?

Variables defined using the var keyword in App.js in a node application are not put into the global namespace as if you had used var in a web page (outside of function scope).

What exactly is the scope of the variables defined using var in app.js?

The top scope is the module (i.e. file). Variables cannot go beyond that. Well, there is a hack, but I do not recommend it.

Each file is the highest scope which would be global

Actually you can use

process.env.USER_DEFINED_VAR

for globally accessible variable between files

The scope of a variable declared using var is local to the function.

Because javascript's only scope is function scope.