Encapsulation is more than just defining accessor and mutator methods for a class. It is broader concept of object-oriented programming that consists in minimizing the interdependence between classes and it is typically implemented through information hiding.
In a object-oriented programming language like Java, you achieve encapsulation by hiding details using the accessibility modifiers (public, protected, private, plus no modifier which implies package private). With these levels of accessibility you control the level of encapsulation, the less restrictive the level, the more expensive change is when it happens and the more coupled the class is with other dependent classes (i.e. user classes, subclasses).
Therefore, the goal is not to hide the data itself, but the implementation details on how this data is manipulated.
The idea is to provide a public interface through which you gain access to this data. You can later change the internal representation of the data without compromising the public interface of the class. On the contrary, by exposing the data itself, you compromise encapsulation, and therefore, the capacity of changing the way you manipulate the data without affecting its users. You create a dependency with the data itself, and not with the public interface of the class. You would be creating a perfect cocktail for trouble when "change" finally finds you.
There are several reasons why you might want to encapsulate access to your fields. Joshua Bloch in his book Effective Java, in Item 14: Minimize the accessibility of classes and members, mentions several compelling reasons, which I quote here:
You can limit the values that can be stored in a field (i.e. gender must be F or M).
You can take actions when the field is modified (trigger event, validate, etc).
You can provide thread safety by synchronizing the method.
You can switch to a new data representation (i.e. calculated fields, different data type)
However, encapsulation is more than hiding fields. In Java you can hide entire classes, by this, hiding the implementation details of an entire API. Think, for example, in the method Arrays.asList(). It returns a List implementation, but you do no care which implementation, as long as it satisfies the List interface, right?. The implementation can be changed in the future without affecting the users of the method.
Think, for example, in the level of abstraction in the concept of a car. A car is complex in its internal implementation. They have several subsystem, like a transmission system, a brake system, a fuel system, etc.
However, we have simplified its abstraction, and we interact with all cars in the world through the public interface of their abstraction. We know that all cars have a steering wheel through which we control direction, they have a pedal that when you press it you accelerate the car and control speed, and another one that when you press it you make it stop, and you have a gear stick that let you control if you go forward or backwards. These features constitute the public interface of the car abstraction. In the morning you can drive a sedan and then get out of it and drive an SUV in the afternoon as if it was the same thing.
However, few of us know the details of how all these features are implemented under the hood. Think of the time when cars did not have a hydraulics directional system. One day, the car manufactures invented it, and they decide it to put it in cars from there on. Still, this did not change the way in which users were interacting with them. At most, users experienced an improvement in the use of the directional system. A change like this was possible because the internal implementation of a car is encapsulated. Changes can be safely done without affecting its public interface.
Now, think that car manufacturers decided to put the fuel cap below the car, and not in one of its sides. You go and buy one of these new cars, and when you run out of gas you go to the gas station, and you do not find the fuel cap. Suddenly you realize it's below the car, but you cannot reach it with the gas pump hose. Now, we have broken the public interface contract, and therefore, the entire world breaks, it falls apart because things are not working the way it was expected. A change like this would cost millions. We would need to change all gas pumps in the world. When we break encapsulation we have to pay a price.
So, as you can see, the goal of encapsulation is to minimize interdependence and facilitate change. You maximize encapsulation by minimizing the exposure of implementation details. The state of a class should only be accessed through its public interface.
I really recommend you to read a paper by Alan Snyder called Encapsulation and Inheritance in Object-Oriented programming Languages. This link points to the original paper on ACM, but I am pretty sure you will be able to find a PDF copy through Google.
Great Response . especially when u summed up your comments in these 3 lines "So, as you can see, the goal of encapsulation is to minimize interdependence and facilitate change. You maximize encapsulation by minimizing the exposure of implementation details. The state of a class should only be accessed through its public interface." .. Nice Job!
@oblivion It means the users of your API, the persons who would actually use it to solve a problem.
@Lealo, it would be very hard to just comment on that. My suggestion is that you open a question about it and make a reference to this post, that way you could get an extensive answer.