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Apparently it used to be considered something you would try and hide, back in the days of the cultural cringe[0], whereas now it can be seen as a bit of a badge of honour. My wife's family descends from a convict bloke whose free wife came out too and got her husband assigned to her. Convicts were assigned as essentially unpaid labour (other than food and a rough bed) to land owners at the time. Given that many were very petty criminals back in Britain (e.g. stealing a loaf of bread) some interpret the arrangement as not much better than slavery, as a means to provide free labour to grow the fledgling colony. Some of the tales of the worst penal institutions (think Tasmania) are truly horrifying. But many convict labourers were granted their freedom over time too. It also had an interesting effect on the labour market, with free settlers finding it hard to get decent pay as farm labour etc. One of the great statesmen, Henry Parkes, was in exactly that position when he first arrived in Aus as a poor settler, and got involved in the protest which eventually turned back the last convict ship ever to anchor in Sydney Harbour. He went on to be elected multiple times as premier of NSW, achieving lots of progress in the state (trained nursing, universal education etc.) before getting the heads of all the colonial states around the table to drive the process of joining to become the nation of Australia. If only we had statesmen / women of that calibre today ... but sadly not.

[0] https://en.wikipedia.org/wiki/Cultural_cringe