require(id) is the CommonJS syntax for importing modules whether that's via their npm package name or a path to a js/json file. When the function is called with a package name like "express". That package is looked up in the node_modules directory and it tries to find an entrypoint in the node_modules/express/package.json file or if a main file isn't specified (as in the case of express) node_modules/express/index.js can be used.

Following the imports from index.js lead you yo lib/express.js where the main exported function can be found:

/**
 * Expose `createApplication()`.
 */

exports = module.exports = createApplication;

/**
 * Create an express application.
 *
 * @return {Function}
 * @api public
 */

function createApplication() {
  var app = function(req, res, next) {
    app.handle(req, res, next);
  };

  mixin(app, EventEmitter.prototype, false);
  mixin(app, proto, false);

  // expose the prototype that will get set on requests
  app.request = Object.create(req, {
    app: { configurable: true, enumerable: true, writable: true, value: app }
  })

  // expose the prototype that will get set on responses
  app.response = Object.create(res, {
    app: { configurable: true, enumerable: true, writable: true, value: app }
  })

  app.init();
  return app;
}

as you can see in the code snippet above x is express' createApplication function since it's assigned to the export variable. As to why you need to call the x function, that's simply express' chosen way to instantiate their application, other packages do it differently.

A module is a bundle of related code.

Express is a module.

Modules can export values (much like object properties have values).

The exported values can be any type of value.

Functions are a type of value.

The value exported by Express is a function.

You can tell because the documentation tells you to call it as a function and also by looking at the source code.

Express exports a function, and in order to use it, you should call that function. To have a better image of what's happening, say you have these files:

function.js:

const foo = () => console.log("Hello Word");
module.exports = foo;

index.js:

const x = require('./function');
// x == foo
x(); // will log Hello Word

And if you hadn't had that module.exports = foo in function.js, x would be equal to {}.