module.exports is the object that's actually returned as the result of a require call.

The exports variable is initially set to that same object (i.e. it's a shorthand "alias"), so in the module code you would usually write something like this:

var myFunc1 = function() { ... };

var myFunc2 = function() { ... };

exports.myFunc1 = myFunc1;

exports.myFunc2 = myFunc2;

to export (or "expose") the internally scoped functions myFunc1 and myFunc2.

And in the calling code you would use:

var m = require('mymodule');

m.myFunc1();

where the last line shows how the result of require is (usually) just a plain object whose properties may be accessed.