The reserve powers are:
The power to dissolve (or refuse to dissolve) the House of Representatives. (Section 5 of the Constitution)
The power to dissolve Parliament on the occasion of a deadlock. (Section 57)
The power to withhold assent to Bills. (Section 58)
The power to appoint (or dismiss) Ministers. (Section 64)
Those powers are generally and routinely exercised on Ministerial advice, but the Governor-General retains the ability to act independently in certain circumstances, as governed by convention. It is generally held that the Governor-General may use powers without ministerial advice in the following situations:
if an election results in a Parliament in which no party has a majority, the Governor-General may select the Prime Minister
if a Prime Minister loses the support of the House of Representatives, the Governor-General may appoint a new Prime Minister
if a Prime Minister advises a dissolution of the House of Representatives, the Governor-General may refuse that request, or request further reasons why it should be granted. It is worth noting that convention does not give the Governor-General the ability to dissolve either the House of Representatives or the Senate without advice.
The use of the reserve powers may arise in the following circumstances:
if a Prime Minister advises a dissolution of Parliament on the occasion of a deadlock between the Houses, the Governor-General may refuse that request
if the Governor-General is not satisfied with a legislative Bill as presented, they may refuse Royal Assent
if a Prime Minister resigns after losing a vote of confidence, the Governor-General may select a new replacement contrary to the advice of the outgoing Prime Minister
if a Prime Minister is unable to obtain Supply and refuses to resign or advise a dissolution, the Governor-General may dismiss him or her and appoint a new Prime Minister.