I find it helpful to view a currency as consisting of two parts. First, currency, as we are used to thinking about it, can be used to exchange goods and services. If all countries used the same currency, trade would be simpler. The second component of a currency can be viewed as a right to buy and sell in a particular country. It is like an admission ticket into a country. Let me explain.
The dollar is the currency of choice in the U.S. For foreigners to obtain the "right" to buy and sell in the U.S., they must purchase dollars. The dollar is then like an admission ticket into America. Once inside the U.S., the foreigners use those dollars the same way they use their currency as they proceed with buying and selling.
Thus, when an American imports a good from another country, and when it pays in dollars, it is giving two things. Those dollars given in payment give that country the right to trade in the states plus something of value to trade with.
So, suppose that we import tea from Sri Lanka. Further, suppose that America comes out of its recession and once again becomes the preferred place of investment for people in other countries, including Sri Lanka. Sri Lankans (is that what you call them) have a greater demand for American investments, and to purchase those investments, they need dollars. They want more access to the U.S., and will pay a higher admission fee into the U.S. When an American gives dollars for tea, it is now giving something of greater value, because the "right" to enter the U.S. is valued more. Consequently, Americans can obtain the same amount of tea for less dollars. The dollars are worth more.
I have learned that by viewing the dollars as a combination of these two parts -- a medium of exchange in the U.S. and an admission ticket into the U.S. -- in combination with the Indifference Principle, international trade and exchange rates become easier to think about.