Currencies not backed by (say) gold are abstract entities with no _objective_ level of value. But one can say that a currency is highly valued if it buys more labor in other countries than it buys within its own country.
At the beginning of this century the U.S. took the lead in automation and mechanization. A dollar could buy more manufactured goods in America than in other countries (because of the location of production), but it could buy far more labor in less-developed countries. Therefore, the dollar was said to have a high value. This was reinforced after WWII -- so many European factories had been smashed during the war, and many of their most brilliant citizens were driven away as refugees or murdered by jealous people of lesser talent.
The dollar started to fall in the 1970s as Europe rebuilt and Asia industrialized, but then the rise of socialist movements threatened the security of investments around the globe -- even in Europe where people feared they might be taxed away. When foreigners bought up dollars they were in a sense trading purchasing power for security. For example, a resident of Argentina might make more
profit from an investment at home, but an investment in the U.S. would be less likely be confiscated by a government. So people were willing to pay a premium to get the dollars needed to invest in America where property rights were more secure.
Right now we have truly bizarre imbalances in the
exchange rates -- when you compare the labor that a dollar can buy in China or India versus America. Trade and free-enterprise tends to reduce these imbalances, so I would not be at all surprised were the dollar to fall hard against these currencies. That is, unless politics once again threatens the security of investments in these countries.
But as foreign countries develop longer and longer traditions of respect for private property, people are going to be decreasingly willing to pay a premium to keep significant portions of their wealth in the U.S. (All the moreso if America itself abandons its economic traditions.)