Thanks for your question. It is a very interesting one which could be answered in many different ways.
Australia is a democracy. Democracy means the people have a say about how they are governed. In Australia the people have their say by electing members of parliament to make decisions for the whole country. These members of parliament represent the people, which is why Australia is a representative democracy.
Australia also has a monarch (the Queen) as our head of state. The powers of the monarch are set out in the Constitution, along with the powers of the parliament and the courts. This means that Australia is a constitutional monarchy.
Australia’s parliament is bicameral, meaning it has 2 chambers. This is similar to the British Parliament as many of the functions and practices of the Australian Parliament are based on British Parliament, also called the Westminster system.
The Australian system of government fact sheet has more information about how Australia is governed.