Has to do with maintaining currency reserves and the denominating of commodities like oil. To put it simply, you have to buy oil in US dollars, because that's what OPEC prices it in. If you're Germany, and you want to buy oil (and you do), you keep a stock of US dollars on hand to buy oil, so you're not subject to the vagaries of the exchange rate. Then you trade on the currency market for more US dollars to replenish your supply. In short, the dollar is artificially propped up on the exchange markets because of dollar-denominated real goods, independent of its value as a currency.
This is why when OPEC has made rumblings in the past of moving to denominating oil in Euros or in a basket of currencies (or even in a new currency that would be traded on the exchange markets), it was seen as provocative.
What happens is that if the dollar starts plummeting and other countries have reason to believe that it will continue plummeting, they're going to dump all the dollars they have in reserve, because:
A. They can buy them back later for cheaper, and in a way if they don't take advantage of the fall, they're screwing themselves. Example: YOu have $100 in US reserves, which is worth 100 Foobucks (hypothetical currency). The dollar plummets, so that eventually $100 is only worth 25 Foobucks. The real-world price of oil is fairly inelastic, save for speculation, so a barrel of oil might shoot up from $100/barrel to $400/barrel. If you hang onto your $100 you started with, your 100 Foobuck investment only buys you 1/4th of a barrel of oil now. If you sold it off and got your Foobucks back as soon as the fall started, you can then buy back $400 for the same 100 Foobucks, and still get the same 1 barrel of oil.
B. If the dollar were to plummet that precipitously (and that's an extreme example), it's likely that OPEC would abandon dollar denomination and move to something more stable. The Euro's not particularly hot right now either, so maybe the British pound or the yen? Or the oft-discussed Petrodollar? The value of the Chinese yuan is also pegged to the dollar, and although it would make Chinese exports ridiculously cheap and popular, it would also kill the PRC's purchasing power and cause soaring domestic inflation in imported materials and goods. So a precipitous drop make cause China to unhook the yuan from the dollar, which would contribute to an even steeper plummet for the dollar. Basically, no one outside the US is going to want to hang on to US dollars if the market deems them not worth the paper they're printed on.
Now, the above is all things that COULD happen, certainly not WILL happen. It would take a perfect storm of monetary policy shifts and market confidence failures to bring all that about. But the potential is terrifying. You know those stories about how a loaf of bread in Weimar Germany cost 10 million marks? Yeah, that kind of terrifying. (Incidentally, while Googling for the rough figure to use there, I noticed a slew of sites selling silver and gold all cite the loaf of bread thing, usually with massively overinflated figures like 430 billion marks...fear sells.)