Thank you for a very interesting question.
The Australian Constitution gives the Governor-General executive power. This means that the Governor-General has been given certain powers to act on behalf of the Queen. These include giving Royal Assent to laws passed by the Australian Parliament and starting the process for a federal election. While these powers are exercised by the Governor-General, in reality they normally operate on the advice of the Prime Minister and ministers, who have day-to-day responsibility for governing Australia.
The power of the Prime Minister comes from the fact that he or she is the leader of the Australian Government. This means they are a member of parliament and lead the parliamentary party or coalition of parties with the support of the majority of members in the House of Representatives.
The Prime Minister has to many important roles. These include: