I did a quick check of the NSW Crimes (Sentencing Procedure) Act 1999, and there seems to be no reference to it (although I only read through the index not the whole Act). It may be a common law device in NSW, or there may be another piece of legislation I didn’t pick up. I imagine pretty much all states in Australia have the same concept, however. It’s conceptually a little different from the deferred sentencing options adn the conditional discharge options referred to by others above.
If my experience elsewhere in Oz in anything to go by, the idea is that the court can impose a penalty now (such as a fine, probation, community service, etc, ) and if you are a suitable candidate such as a young first offender, the court can order that the conviction not be recorded. Prison sentences are usually excluded from this process as too serious to be “not recorded”.
“Not recording a conviction” is a confusing concept because of course it is recorded by both the courts and the police. If you are convicted of another offence later, it will generally be brought up by the prosecution in dealing with your antecedents so that the court will take a much dimmer view of you.
What it means, however, is that you typically don’t have to mention it in those forms which commonly require you to do so, such as job applications, passport applications and so. You can say “no” to relevant questions about whether you have been convicted of an offence without being guilty of fraud.
The idea is that you can get punished for the offence, but you don’t have it hanging over your head in such a way as to prevent all sorts of things that would advance your rehabilitation like getting a job. If you got caught with a little weed, you might get fined, but if it is a first offence the court doesn’t want that to result in your getting the sack or being stuck in the ranks of the unemployable for ever.
I say “typically”, because some employers get around it by asking if you have ever been charged with an offence, and for some jobs the free pass does not apply - common examples include teachers, police officers, and so on.
So the above stuff is just general and dependent upon the particular circumstances and jurisdiction - if you have a real issue with this, consult a lawyer - I am not yours and this is not legal advice.