A republic is a country where power is completely in the hands of the people. An Australian republic would make our system fully democratic and fully Australian.
In Australia today, the people have no say in who is the head of state - instead, the head of state is the King or Queen of England. The Governor-General is only their representative to act on their behalf and has to approve every law made by our Parliament, every election and the appointment of every government.
For Australia to become a republic, we need to replace having a King or Queen and a Governor-General with having an Australian as our head of state - someone chosen by Australians to serve Australia.
An Australian republic would keep a Prime Minister as our head of government and a Parliament to make laws, but the person who is our head of state would not be an English King or Queen, they would be an Australian, chosen by Australians.