Now I am confused. How can the member nations of the Commonwealth of the Brittish Empire, be soverign nations, yet have their official head of state be the ruler of another country? And why is the queen on half of the world's money?

Because they choose to have it that way. Soverign democratic nations are allowed to do that.

The Queen is on half the money, because for a long time her predecessors ruled half the world. As for the first question, the countries are autonomous, they make their own decisions, and operate without control or input from Great Britain. However the Queen is the figurehead of the nation. In Canada her, or her representative here (the Governor General) signs all bills into law and makes everything official. That being said, it is rare to non existent occassion that the Governor General/Soverign will veto a bill. The reason she exists is that historicaly the nations were ruled by Great Britain and unlike American Independance it was granted, not won in battle. So the ties to the UK still exist in the member countries.

I am not being argumentative, just trying to understand a different system. Why would a country want a foriegn leader to be their ultimate leader? Is it becasue there is such a common history between the two that a situation would never arise where the two would disagree? Is there a way to overrule the veto of the Governor General?

Umm as far as i know the only person who can overrule the Governor General is the Queen herself. The common history is the reason for the connection to the British monarch. The majority of Canada's symbol's and traditions are traceable to England. The monarch granted us our indapendance, so there was never any animosity between the two nations. I guess in 1867 when the country was created as an independant nation, the fathers of confederation wished to keep the monarch, as a sign of the ties which they shared with England. She serves no real purpose in the present day, other than as a figure head.