The dollar is the currency used to purchase oil and illegal narcotics around the world. Regarding oil, if Iran decides to sell its oil in a currency other than oil, then there will be less global demand for the dollar to use to buy it.
If there is less demand for the dollar, then its value will decrease. If the value of the dollar decreases, to the U.S. consumer that means that prices will go up, massive importers like WalMart and Target will have their prices rise. Right now, it possible to get a lot of stuff cheap overseas because the dollar is strong, and sell it here to you for a low prices in terms of the dollar. That will fuel inflation in the U.S.
If the dollar decreases, it also means that U.S. exported goods will be cheaper, so it will help our exports. And suddenly, coming to the U.S. for vacation will be cheaper, so the tourism business will improve.
A falling dollar will have big ramifications for other nations whose currency is pegged to the dollar. Their currencies will fall in value, as well. So it is rather a big threat on Iran's part.
Threats seem to be a Middle East specialty.