Selling in local currency means showing the price in pesos to a Mexican buyer and in euros to a German one, and charging in that currency. The buyer doesn't need to convert in their head or find out the real amount only when the statement arrives.

You gain in two places. In conversion, because it removes the moment of doubt in front of a foreign price. And in approval, because a charge in the card's own currency looks far more normal to the issuing bank than a cross-border charge.