A domain name is simply the address on the internet for your website. Examples of domain names are google.com qantas.com.au and apple.com.
Each domain name ends in a domain "extension". The most common domain extensions in Australia are .com and .com.au, but there are many others.
Every domain name must be registered with a relevant authority (based on the domain extension), and each authority can impose different criteria on the registration. For example, anyone in the world can register a domain ending in .com, but only Australian businesses can register a .com.au domain.
There are often disputes over domain names when a person registers a domain and another person wants to use it. Generally, the first person to register the domain name will have the right to use it, so it's important that you register domain names that you may want to use in the future. A good start would be your business name in the .com and .com.au extensions. (eg. yourbusiness.com and yourbusiness.com.au)
You can learn more about .au domain names with the videos below, provided by the auda (the .au Domain Authority).
The benefits of .au domains
Australia's bond with .au
The structure of .au and eligibility criteria
What is WHOIS?