What is a mutable member?

One that can be modified by the class even when the object of the class or the member function doing the modification is const.
Understanding this requirement implies an understanding of C++ const, which many programmers do not have. I have seen large class designs that do not employ the const qualifier anywhere. Some of those designs are my own early C++ efforts. One author suggests that some programmers find const to be such a bother that it is easier to ignore const than to try to use it meaningfully. No wonder many programmers don't understand the power and implications of const. Someone who claims to have enough interest in the language and its evolution to keep pace with the ANSI deliberations should not be ignorant of const, however.