This statement of the role of the Governor-General is taken directly from British Monarchy website.
Statement on the Governor-General from Buckingham Palace.
The Governor-General is The Queen’s representative in Australia. As such, he or she performs the same constitutional role in Australia as The Queen does in the United Kingdom.
The Queen maintains direct contact with the Governor-General, although she delegates executive power to him or her in virtually every respect.
The present Governor-General of Australia is Her Excellency Ms Quentin Bryce AC.
Duties which the Governor-General carries out in the name of The Queen include opening and dissolving the Australian Parliament; commissioning the Prime Minister and appointing other Ministers after elections; giving assent to laws when they have been passed by the two Houses of Parliament; and appointing Federal judges and ambassadors and high commissioners to overseas countries.
The Governor-General is the Commander-in-Chief of the Australian Defence Force, although in practice he or she acts only on the advice of Ministers. As Commander-in-Chief, the Governor-General has an important ceremonial role to play.
He or she attends military parades and special occasions such as Anzac Day, and presents colours and other insignia to units of the Australian Defence Force.
As The Queen’s representative, the Governor-General also receives and entertains official visitors to Australia; conducts investitures at which people receive awards for notable service to the community; and entertains many Australian citizens active in the life of the community.
Both the Governor-General and The Queen send congratulatory messages to people celebrating notable birthdays and wedding anniversaries.