The point of it is two-fold: separation of concerns, and DRY. But the reason it so ugly on the web when it produced elegant code for GUIs is the reason that web controller schemes are not MVC.
Errm, it's a pattern often used for UI (CLI and GUI) programming that was first commercially introduced in Smalltalk-76 (in 1976). [This predates Windows and Mac by many years.]
MVC can be done -with varying degrees of difficulty- in any computer language. You don't even need a web development framework to implement it! ;-)
iOS/OS X seems to do real MVC, with lightweight reusable view objects managed by ready-made controller classes. The obvious benefits are minimal memory and streamlined data flow. You only ever make/use the view objects you really need, you can recycle them to save memory, and - in OS X especially - controller objects include useful ready-made convenience methods.
Web frameworks often seem to do something that looks like MVC if you squint and don't think too hard. But when you're forced to use separate languages for logic (js), markup (HTML), and view design (CSS), and handle separate client/server environments, and there's inevitable overlap between all of the above (jquery etc) because stuff doesn't "just work", and you probably have yet another layer as a DB driver, it gets very complicated very quickly - to no great benefit.
The web has become a snarly ball of warty epicycles. That's why native is so popular - you get one common language for logic, views, and data, with a clean-ish interface to a remote server if you need one.
When everything works together like that, you can think seriously about MVC.
When the core concerns are all over the place already, it's a mess before you even start.
Which is not to say you can't work with it and build cool stuff - more that you can't just airdrop in a design pattern from a different tradition without thinking really, really hard about what, why, how, and what happens a year from now.
Separation of concerns and DRY are both good. MVC doesn't succeed at either, except in idealized corner cases.
[1] A lot of widgets in Windows, for instance text fields, encapsulate the view (it's where the text is displayed), the model (which keeps the text in the control), and the controller (the widget handles the UI for entering text, catches and handles the mouse, etc.).
(In angular, when you edit data in the view, the model is immediately updated, which is why it's MVVM and not MVC.)
Every interviewer has their own pet question that the candidate is COMPLETELY UNQUALIFIED if they don't know.
My short answer to "What is MVC?" is that it's a popular web development trend, but without much substance to back it up. Every MVC project that I've been supporting/maintaining was a nightmare, taking 3x-5x longer to get stuff done than what I consider reasonable.
MVC = Model-View-Controller. It's usually for web development. You structure your code in a way that separates the data logic (Model), the user presentation logic (View), and the glue that holds the bits together (Controller).
There are many popular MVC frameworks that let you churn out a lot of mediocre websites quickly (angular.js, Ruby on Rails, Zend, Django(Python), and many others). The MVC framework does a lot of routine coding for you, but it comes at a price. The code can become a nightmare to maintain, especially if you use the MVC framework incorrectly. If you do something outside what the MVC framework provides, it can become a handicap rather than a help. The MVC framework usually demands you write your whole application in its preferred style, such as spreading out your code in various directories with forced naming conventions. MVC frameworks tend to be poorly documented compared to the underlying language (For example, compare the zend documentation to php.net).