Why would people move to Australia?
This question appears a bit vague. Do you mean in today's time, or are you searching for some kind of historical event and related reason? I'll answer it as if you are asking about current times.
For me, moving to Australia would be appealing because the country speaks the same language that I speak -- English. Being able to easily communicate with the local population would make moving there easier. There would still be customs and nuances to learn, but at least the language is not a barrier.
Australia is also a wonderful country to live in, if a person is an outdoor lover. Australia has some of the world's best beaches and surfing. The diving (SCUBA) along The Great Barrier Reef is unparalleled. Australia also has a lot of unique wild life that exists no where else in the world.
Another good reason to move to Australia is health related. Australia has one of the lowest air pollution levels of any country in the world. The climate is temperate and warm for most of the year, which means no harsh winters to suffer through. Lastly, Australia's healthcare system is considered one of the best in world.
If a person is tired of crowded spaces, Australia would be a great country to live in. The continent has an extremely low population density.