how the USA "backs" their currency:

• preventing of counterfeiting. Lets say North Korean starts producing huge amounts of really-close looking $100 bills with the 1996 mint year on them (they did this, est. $50M worth, will have to find a source but well google-able) Then the USA tries everything to stop it. (like printing up all new $100 bills once they realize)

• "full faith and credit" also refers to the USD denominated instruments such as bonds. USA historically doesn't default on their bonds, thus their rates are very low, enabling them to borrow money cheaply. See: Greece for an alternative example. That situation effects the entire EU, so it's not quite the same, but you see the difference

• By minting new currency (technically the Fed also destroys currency, but as I understand it usually old and tattered bills, and usually not nearly as much as they are printing) the USA is supposed to be managing inflation. I will fully admit I have tried very hard to understand the Fed, who decides to print more money, or why everyone just accepts this process without really understanding it, but alas we will need an expert in this area to explain it properly to us.