mental ray shader is C/C++ code that is invoked by the mental ray core when a ray hits an object. The name ``shader'' is used by hysterical reason, I think ``Plugin'' is much better word nowadays. mental ray shader gives us a lot of freedom for users, but, I think we do not need to write a custom shader in most of the cases.
The meaning of 'gives us a lot of freedom' is when a ray hit an object, a user could almost everything by a shader. For example, when a ray hit an object, mental ray can send an email from the shader. (I believe that mental ray designer does not recommended this kind of side effect usage, but, a shader is just a plugin and it should be possible.) You can do anything means also it is difficult to handle the shaders. mental ray was developed for a long time and takes care of backward compatibility, this contributed for its complexity.