Overriding "/user" page with Feature (Drupal 7)
Features is the way to move configuration data between different environments, or at least the most typical. But in your case you need to move functionality, not simple configuration (as what you want to achieve can't be done just modifying configuration).

Features takes some Drupal objects as Views, permissions, roles, content types, panels and so on an put them into code that can be later imported to another Drupal instance. This is considered configuration because even when  this kind of objects add functionality to the site you have added it configuring some modules. 

So, if you can manage to achieve your desired functionality (I suppose using Panels and others modules) you may export that configuration using Features. And I say may because not all configuration can be exported this way (most yes).

In your case probably you'll need a custom module that menu_alters the /user URL and uses a custom page callback that adds what you need. But what you need is too broad to explain in an answer here.