I'm a little confused on the "subject" question.

According to my Cambridge Factfinder (which could very well be wrong), The "Head of State" of Canada is the British monarch, represented by the Governor General. What does this mean? How can the British monarch be Head of State of a country whose citizens are not her/his subjects? Is my CF totaly out of date? (Date of publication, 1993.) Ooohhh, I'm so confused...