Australia is a liberal democracy. That means that it has a form of government that is elected by the people. In the case of Australia, the democracy follows a parliamentary system with a prime minister who is the head of government. The official head of state is the monarch of England, but she is merely a figurehead with no real authority.
Like most liberal democracies, Australia has a capitalist economic system. Its system is something of a mixed economy which is mainly a market economy but with aspects of a command economy mixed in.