Wikipedia says:
MVC provides front and back ends for the database, the user, and the data processing components. The separation of software systems
OK.. first the terms:
If you read GUI Architectures and research the MVC pattern in general, you will understand that MVC is not about separation of backend and frontend. Especially when it comes to MVC-inspired patterns, that we use for web applications.
The goal of MVC and related patterns is to separate presentation from domain business logic.
Here are the basic responsibilities of MVC parts:
Let's take an example:
This all can be done with client-side JavaScript. You can have MVC triad running "frontend"! At the same time, the "backend" which provides REST API is an MVC-like structure. Only this time the View is generating JSON responses, instead of HTML.
*Conclusion: You can use MVC pattern both on backend and frontend.**
Since you have been building some applications with Rails, your understanding of MVC might be a but distorted. The reason I say this is because, since RoR was initially made as a prototyping framework (notice all the scaffolding and other features for generating throw-away code), and because of its origin, Rails is actually implementing a very anemic version of MVP.
I call it "anemic", because they nerfed both View (it should be a passive object in MVP, not a simple template) and Model Layer (yes, it is supposed to be a complicated layer, not a collection of ORM instances).
I would recommend for you to read two publications to get a much better grasp on the subject:
The second one is as close as you can get to initial definition of pattern. That, together with "GUI Architectures" article, should provide you a solid footing on the subject. And the PoEAA book (hard read, btw) would give you context in which to expand it.