What is a good answer to this interview question "What is the purpose of Object Oriented Programming? What are the benefits?"?

There was structured programming with structures which held values in one structure. But you had to find the methods yourself. With object oriented programming the methods declared as part of a class so when programming the IDE will tell you the methods available for an object. ( Microsoft's name for this is IntelliSense. )

Object-Oriented Programming (OOP) is an attempt help developers create software that better conforms to principles of quality software. This includes high cohesion and lose coupling. It helps the software designer / developer concentrate more on the problem being solved. A key characteristic of OOP is abstraction: In designing a class, the developer pays attention to the attributes and methods useful in the solution, and disregards attributes and methods that are irrelevant to the solution. 

In the words of one of my professors, it allows "the language of the solution to be closer to the language of the problem." 

In my opinion, the main benefit of OOP is it improves the programmer's thinking. It trains the mind. 

Comment on another answer: The phrase "structured programming" doesn't refer to putting data in structures. It refers to the organization of the control flow -- the parts of the program with the imperative statements.

 I consider it a poor question because I wouldn't exactly say that it has a purpose, per se.

One way to answer it is that OOP allows encapsulation, inheritance, and polymorphism, so you look up each of those terms.  

But the real question is: How much experience do you have with examples of OOP in your assignments?  You should be able to relate attributes of OOP to those examples.  If you haven't had such experience, you really shouldn't try to get a job at would ask you about OOP in an interview.