It is the building block underneath purchasing-power-parity. If gold is cheaper in one market than another after conversion, someone buys in one and sells in the other until the prices meet. For a freely shipped, storable, homogeneous good the logic is tight.
It fails wherever those conditions fail: transport costs, tariffs, taxes, local wages embedded in the price, brand pricing and non-tradable services all drive permanent wedges. That is why the same car or haircut costs different amounts in different countries indefinitely.
In financial markets the law holds much better, which is what makes triangular-arbitrage and covered-interest-arbitrage work: the goods are identical and shipping is instant.
Example: gold trades at $2,400 an ounce and GBP 1,890 in London with GBP/USD at 1.2700. The London price is $2,400.30 converted, a 30-cent gap that is inside dealing costs and therefore no opportunity.
Related: purchasing-power-parity, triangular-arbitrage, covered-interest-arbitrage, big-mac-index