As the Commonwealth of Australia is a constitutional monarchy, the Governor-General represents the head of State, Her Majesty the Queen of Australia. By the constitutional conventions of responsible government, however, the Governor-General only exercises the Queen's functions on the advice of the Executive Council, responsible to the elected House of Representatives.
However by convention the queen appoints the governor general on the prime minister's recommendation, and the governor general will always follow the advice of the government of the day.