I think i can give you a good idea of it, seeing as both my parents are in the healthcare industry/used to work in hospitals.
Basically we have a system that is based around England's system, which is that the government pays for your medical bills, aswell and surgeries, hospital stays, medications. But this is only if your registered with a healthcare provider, like, for example my family is with one called MediCare. And they really do take care of you.
BUT. We have a massive problem, particularly in New South Wales (one of the states) with our public (government run) hospitals. We've been having a whole bunch of crises with our public hospitals in emergency room waiting times and under staffing and lack of supplies. And at the moment the biggest problem is elective surgery waiting times, which in some cases, have people waiting up to 3 years for really simple procedures.
So basically, in a nutshell, Australia certianly has a very good healthcare system, with good doctors and junk, and the government will pay for you if your sick, but at the moment they aren't managing it very well.
Hope that helps you out, and wasnt too confusing.