The three main factors that determine the value of money are exchange rates, the amount of dollars held in foreign reserves, and the value of Treasury notes.
The most important single factor determining the value of money is the basic rule of supply and demand. The more demand for a given currency or item, the more that currency or item is worth. That is especially the case when demand exceeds supply. Because every country maintains its own currency, and because the political and economic situation in each country varies, sometimes minutely, and sometimes massively, the value of each country's currency varies accordingly. The less confidence in a particular currency, the weaker the demand for that currency and the lower its value. When a foreign currency is determined to be worth a specific amount of the U.S. dollar, to use one example, the value of the American currency is measured in how much of the foreign currency is needed to buy a single dollar. In other words, it may require ten thousand Indonesian Rupiah to buy one U.S. dollar (the actual exchange rate when I was last in Indonesia some years back). The value of American money, then, is much greater than that of the Indonesian currency.
A second factor used to determine the value of money involves the amount of a given currency--we'll use, again, the U.S. dollar for illustrative purposes--held by foreign nations in their central repositories, known as their "reserves." Many countries maintain supplies of foreign currencies to hedge against radical shifts in exchange rates. China holds over $1 trillion in U.S. debt, which it uses in part to keep the value of its own currency, the renminbi, or yuan, lower than the dollar. It does this because its economy is highly dependent upon exports to large markets like the United States. If the Chinese currency was equal on a one-for-one basis to the U.S. dollar, its exports to the United States would cost more than is currently the case. That would mean that Chinese-produced goods would be more expensive for American consumers, which would drive down demand for those goods, which would hurt the Chinese economy. A more powerful dollar keeps Chinese exports more affordable in the United States, while the dollar's value makes American goods more expensive for Chinese consumers. The result is a trade imbalance favoring China.
A third factor determining the value of money is another extension of the fundamental principle of supply and demand: U.S. Treasury notes and bonds. The principle of a bond is simple: an individual or a foreign government buys U.S. Treasury notes or bonds that will mature over a specified period of time (usually ten years in the case of notes), at the end of which the note or bond can be traded in for a specified amount that includes interest on the original investment. Foreign and domestic purchases of U.S. Treasury notes, bonds, and bills influence the value of the dollar because the more such financial instruments are purchased, the more confidence those consumers and foreign governments have in the future of the U.S. economy.
The value of money can be arbitrary, and it can be tied directly to an item considered particularly valuable in and of itself. This is one way of pointing out that the value of money can, and used to be, tied to the value of gold. Paper money is just that: paper. Until the Great Depression, when the dollar was disconnected from the value of gold, its value was determined by the price of gold. After the U.S. dropped the use of "the gold standard," the value of the dollar was dictated by the federal government's requirement that the dollar be accepted as a form of payment.
It is precisely because the value of money can be so arbitrary that some people believe the dollar should once again be tied to the value of gold. That is unlikely to happen, but it does illuminate the fragility of the concept of money. Some Americans worried about the future political and economic stability of the United States buy gold because of that precious metal's enduring value. They store it away in case the value of money declines precipitously and a panic ensues across the nation.
The first factor, and most important, is the balance of trade and investment. This is determined by the gap in exports and imports for a country. This is essentially like supply and demand. If the United States is exporting more products, there is more of a demand for the US dollar. The importing country will then have to convert their currency to dollars in order to pay for the products. The second factor would be market psychology. If unemployment would grow, and production would decrease, the value of the dollar would decrease. Foreign countries may sell their bonds that are in the US dollar in return for their local currency. The third factor would be economic indicators, like GDP, CPI, and payroll data. If the economic indicators indicate that the US economy is growing, often the value of the dollar will increase.
During the recession of 2007, the government intervened and by increasing spending and issuing more debt (bonds). By doing so, they hoped to increase jobs, so more products were produced and more things were purchased by consumers. By selling more bonds, they essentially printed more money, flooding the market with dollars and decreasing the value of the dollar. So, the sentiment was negative, and the supply of the dollar was great, driving the value of the dollar down.