Explain why a class might provide a set method and a get method for an instance variable?

A class might provide a set method (setter) and a get method (getter) for an instance variable in order to encapsulate the internal implementation of the class, and to isolate that implementation from the public interface of the class.

Even if the setter and getter does no more than directly set and get the instance variable, the public interface should use that paradigm in order to allow for possible future alteration of the implementation, while minimizing the impact of doing so.

Proper OOD/P (Object Oriented Design/Programming) should always make the implementation be private, even for derived classes. This reduces error, and reduces "lazy" coding techniques.