AngularJS is the client side Java Script Framework and works based on MVC design pattern. Ruby on Rails is server side application framework based on MVC design pattern. The diagram below is a quick representation of how Angular JS works seamlessly with RAILS MVC.
The power of Angular JS is the client side data manipulations which we use for various User Interface Use Cases like Lists, Refine Search, Graphical Data Representation etc and present the Web Application to the user as a Single Page Application.
The Angular JS Controllers interact with RAILS Controllers. The object data from the RAILS Model (M) is passed to the Angular JS Controllers via Rails Controller(C) using Restful API services. The view part of the application is the Angular JS framework in MVC design pattern, dropping the View in Rails.
This way the true potential of Angular JS is utilized for building the Single Page Application and Rails is capitalized for its server side implementation using its Models and Controllers. The layers interact using Restful JSON API services.