Backbone is an object-oriented library that can increase maintainability for so-called single-page applications. E.g. it's often used in an architecture which pairs a dynamic web service with static HTML templates, CSS, and JS (no dynamic server-side HTML generation). In this way it is similar to ExtJS/YUI, but generalizes those widget-centric frameworks.
It's not for tightly-scoped JS enhancements.
In terms of patterns, it adheres mainly to the Model-View-Presenter pattern (embodied in the Model class, the HTML template, and the View class respectively). Switching between logical pages in the single-page app is supported by the Router class (which implement the front controller pattern). Data persistence/retrieval is oriented toward RESTful web services (this is customizable) and therefore pairs will with ActiveRecord-based server frameworks like Rails. The separation of concerns it encourages increases testability, and also allows it to pair well with asynchronous module loaders (e.g. RequireJS).