Answer
According to several sources, including the TNG novel "Balance of Power", latinum is described as being so dense and complex that the replicators are unable to restructure matter into a form that duplicates it. In its natural state, latinum is a liquid which is mined from certain types of nebulae. It is pressed into gold in order to make it more usable as a means of currency.
Of course, the explanations came later. Originally it was simply a story element created as a means of having non-credit monetary transactions in a universe where a replicator could create anything you want.
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