The basic principle is that the Australian Federal Government subsidises healthcare by a fixed amount for each procedure. So iirc, it was AUD$45 for a visit to the GP. That's enough for some GP practices to be able to offer a free service (referred to as "bulk billed" because they only billed the government). Obviously those services become popular, so to get a free appointment you have to wait a while. Or, you can pay a bit yourself to get an appointment with a doctor who charges more than the government rate and are therefore less in demand.
In Australia I could usually get an appointment next day if I paid $25-50 or so. In the UK it was usually a 1-2 week wait, but free.
This goes for everything (except dental care for some reason, I don't know what's up with that). So an X-Ray costs $200, or nothing if you can wait until next week. And so on.
Health insurance covers the additional costs, and I paid $25/month for a plan that meant if anything serious happened I'd be liable for the first $250. And it also gave me dental cover, so I could claim some (but not all) of my dental care from my health insurance - a net gain for me most years.