Once you get beyond small programs, you run into software architecture questions, which touch issues of maintainability and complexity. One of the techniques we have to manage this complexity is to break the program into components, smaller pieces that couple to each other loosely. This limits the impact of a change, since a change in one component is less likely to require changes in other components. At least that's the hope.
There's lots of ways to decompose a program, each with its own strengths and weaknesses. MVC is a particular decomposition that is useful for interactive applications. The components are named Model, View, and Controller. An example of an advantage of this decomposition is that you can apply a different user interface (e.g. a command line one) by exchanging the View, without needing to change the Model.
Other answers here have focused on MVC as it applies to web development. But MVC is from the 70s, predating the web by many years! If you look beyond the trend, you see ideas rooted in an effort to architect software well, and see MVC as just one design, one particular decomposition. The key idea is not MVC itself, but the principles behind it. Being able to place ideas into larger contexts shows mastery, in my view.
There's lots of ways to decompose a program, each with its own strengths and weaknesses. MVC is a particular decomposition that is useful for interactive applications. The components are named Model, View, and Controller. An example of an advantage of this decomposition is that you can apply a different user interface (e.g. a command line one) by exchanging the View, without needing to change the Model.
Other answers here have focused on MVC as it applies to web development. But MVC is from the 70s, predating the web by many years! If you look beyond the trend, you see ideas rooted in an effort to architect software well, and see MVC as just one design, one particular decomposition. The key idea is not MVC itself, but the principles behind it. Being able to place ideas into larger contexts shows mastery, in my view.