It holds value because there is a limited amount of it (as controlled by the US treasury) and there is a trade balance. In other words there are only so many dollars in the world, and if you want to buy a John Deere tractor (made in the USA) then you are going to have to give John Deere some US dollars for it. If all you have is Euros, then you are going to have to trade your Euros to somebody who has US dollars so that you can buy your tractor. Since there is a limit to the total number of dollars floating around, someone won’t be willing to give them up for free. They are going to want a good number of Euros in exchange for their dollars. It is this exchange rate that defines what the value of the dollar is.

Now if the treasury decides to go and print a whole bunch of new US dollars, then the value of all of the dollars in circulation declines. They are diluted, in other words, by the new US dollars. The government would like to avoid this situation however, because it causes the price of commodities like gold, oil, etc to skyrocket. People tend to get mad when this happens.

Thats basically how it works. You are right, currency is really just paper that is only backed by good faith. That sure is a strange concept, but that is how modern economics works. The US dollars are not backed by commodities, but by the hard work and manufacturing output of US citizens.