What's the meaning of following and what's the purpose?

I think you are more concerned about this line public MyException(string str):base (str) the main purpose of the above line is to call the base class exception constructor with the argument you specife to create the instance of MyException class. This is often know as base member initialization.

Often you derive exceptions to create your own exceptions. It's commonly used if the exception types already provided won't suffice for your needs, in which case you derive exception classes for custom error types.

Your code highlights a class definition (MyException) derived from another class (Exception). Doing so makes your derived class (MyException) inherit public or protected members/methods from the base class (Exception). Inheritance is a very important OO concept. The purpose is to share common behaviors accross multiple class. Have a look here http://www.dummies.com/WileyCDA/DummiesArticle/id-1038.html for a brief explanation on inheritance.