Django/Rails etc are server-side MVC frameworks. Angular/Backbone etc are client-side Javascript MVC frameworks. Django/Rails and Angular/Backbone work together - in a single-page app, usually the server-side MVC will serve the initial HTML/JS/static assets once, and then once that is done, the client-side router will take over and handle all subsequent navigations/interactions with your app.
The difference here lies in the concept of what a "single-page application" is. Think about how a "regular" web Django/Rails website works. A user enters your app, the backend fetches data and serves a page. A user clicks on a link, which triggers the server to serve a new page, which causes the entire page to reload. These traditional types of websites are basically stateless, except for things like cookies/sessions etc.
In contrast, a single-page application is a stateful Javascript application that runs in the browser and appears to act like a traditional webapp in that you can click on things and navigate around as usual, but the page never reloads, instead, specific DOM nodes have their contents refreshed according to the logic of your application. To achieve a pure Javascript client-side experience like this in a maintainable fashion really requires that you start organizing your Javascript code for the same reasons you do on the server - you have a router which takes a URL path and interacts with a controller that often contains the logic for showing/hiding views for a particular URL, you have a model which encapsulates your data (think of a model as roughly one "row" of a database result) which your views consume. And because it's Javascript there are events going on, so you can have your view listen for changes in it's associated model and automatically re-render itself when the data is updated.
Also keep in mind that you don't just have one view on the client side, there are usually many separate views that make up a page and these views are often nested, not only for organizational purposes but because we want the ability to only refresh the parts of the UI that need to be refreshed.
The intro to Backbone is probably a good starter on the topic: http://backbonejs.org/#introduction