what does the operator string() { some code } do?

It is an automatic type conversion operator. This class you are talking about can be implicitly converted to a string. This link might help you with a few more examples.

operator Type() { ... }

is the (implicit) conversion operator. For example, if class Animal implements operator string(), then the code

Animal a;
...
do_something_with ( (string)a );

will become something like

do_something_with ( (Animal::operator string)(&a) );

See http://publib.boulder.ibm.com/infocenter/comphelp/v8v101/index.jsp?topic=/com.ibm.xlcpp8a.doc/language/ref/cplr385.htm for some more examples.

If just returns a string represantation of your current object, e.g. for printing it on the console.

It's overloading the conversion operator. A class which has the function

operator string();

defined can be converted to a string.