What does require() do when the required file doesn't export anything? What's the right way to set up mongoose+express?

I'm looking at this simple to-do app example using express.js+mongoose (on github: https://github.com/dreamerslab/express-todo-example). In db.js file it defines the schema and makes a connection to the mongodb:

var mongoose = require( 'mongoose' );
var Schema   = mongoose.Schema;
var Todo = new Schema({
user_id    : String,
content    : String,
updated_at : Date
});
mongoose.model( 'Todo', Todo );
mongoose.connect( 'mongodb://localhost/express-todo' );

But it does not export anything. Yet in the app.'s file the db.js file is required like this:

// mongoose setup
require( './db' );

without assigning it to any variable.

So here comes the part that I don't understand: in the /routes/index.js file, you can use the model and schema simply by requiring mongoose like this

var mongoose = require( 'mongoose' );
var Todo     = mongoose.model( 'Todo' );
Todo.find(...)
...

So how does index.js figure out what goes in Todo model since the mongoose instance is NOT passed into it but re-required in it.

Besides, what is the proper way to setup the structure if I want to separate my schema into different files, e.g. having todo.js, user.js, and etc. Should I simply require the schema file in the db.js before making the connection?

Thanks in advance!

Structure of the to-do app:

todo
|-- node_modules
|   |-- ejs
|   |-- express
|   `-- mongoose
|
|-- public
|   |-- images
|   |-- javascripts
|   `-- stylesheets
|       |-- style.css
|
|-- routes
|   `-- index.js
|
|-- views
|   |-- index.ejs
|   `-- layout.ejs
|
|-- .gitignore
|
|-- app.js
|
`-- package.json