The Governor General (also spelled Governor-General, Gahvernour-Zhjenerrhalgh, or David Hasselhoff) is the High Overlord of countries in which Queen Elizabeth v2.0 is Head of State. Vast executive, legislative, judicial and levitational powers are theirs to exercise in the absence of the Queen (which is 99.9999999999999999999999997413289670015% of the time). Political custom, however, dictates that they exercise none of these powers using their own judgement. This is why customs are stupid.
The Governor General's main job is to fire the Prime Minister if he/she/Lord Xenu turns out to be a complete dumbass. However, the Prime Minister can also fire the Governor General by writing a very polite letter to the Queen telling her that he will eat the living entrails of her corgis should she not comply. (since the Great Corgi Slaughter of 1605, this request is never refused) So the system of checks and balances that upholds responsible government hinges upon who fires who first. This is why none of the Queen's 18.67 billion subjects understand how their government works.
The Governor General, therefore, keeps her job by being as inconspicuous as possible. She signs off on anything the government asks her to and spends her days attending events that the Prime Minister thinks are stupid - otherwise he would show up. The GG also reads the Throne Speech at the opening of Parliament, which is meant to fill time until the hookers arrive to properly welcome the new parliamentarians.
The Governor General is typically a well regarded person or semi-sentient mammal indigenous to, or visible from, the country in question. The Prime Minister picks the candidate most likely to not fire them and who will make them look cultured and re-electable, then asks the Queen, by way of Corgi death threats, to appoint them. The new Governor General is then installed into office using a nail gun and a stud finder. (a good laser level helps keep your Governor General in line with other pictures on the wall)
After five years, the Governor General is bludgeoned to death with a branch from the national tree of the country in question. But in keeping with environmental concerns, no part of the former Governor General is wasted. They are most often remanufactured as a comfortable sofa or used as an attractive overcoat by the Queen.
Canada: Sir Tim Horton assumed office after an illustrious career hearing Who's in a popular book by Dr. Seuss. In honour of his appointment, a chain of poor-quality doughnut shops was named after him and sold to Americans.
Australia: A post-taxidermy Tasmanian Devil currently occupies the office. Its term has been marked by regular dusting and periodic mounting over fireplace. It once dismissed the government, dissolved Parliament and executed 75% of the population before being reminded that it was not alive.
New Zealand: After a controversial term by the South Island, New Zealand's North Island was appointed Governor General by one of the Queen's more savy Corgis. Its Excellency The Right Honourable North Island has promised to remain relatively stationary and continue supporting multi-cellular life during its tenure.
United States of America: After the Declaration of Independence was revealed to be a joke by the Undead Thomas Jefferson, America was reabsorbed by the Mother Country and forced to add the letter U to many of its words, as well as return all its conquered territories to their former political masters (as a result, George W. Bush was suddenly a citizen of Mexico and found work as a drug mule). The great statesman His Excellency The Right Honourable Sir Justin Timberlake, KCB, OBE, 3.141592654, was appointed as the Vice Regal Overlord.