An ABN identifies your business and once registered it is available to the public on the ABR (Australian Business Register) where anyone can do a search for your ABN, see what type of entity you are trading under, the date you registered, if there is a business name linked to the ABN, and if you are registered for GST.
The ABR does not show your personal details to the public but has them on file. To register your ABN go to abr.gov.au
It’s not compulsory to have an ABN however this does create problems with accessing Govt sites and if you are a contract worker 47% of your income may be withheld by your customer.