The value of our money, both within our country and outside the country, is determined by supply and demand.
Within our country, the value of our money is determined in large part by the price level. If the price level goes up, there is inflation and the value of our money goes down. This is determined largely by the forces of aggregate demand and aggregate supply.
Outside the country, the value of our money is referred to as the exchange rate. Our money has a different value with respect to every other currency in the world. What determines the value of our currency in this case is also supply and demand. When there is a high demand for our currency (like if people want to obtain dollars to buy American goods and services or to invest in the US), the value of our dollar goes up. When we use dollars to buy foreign countries’ currencies (so we can buy exports from them) the supply of dollars goes up and the value of our money drops.
Supply and demand, then, is the main determinant of what our money is worth.