Currencies like Euros and Dollars are traded on the world market all the time, every day. Most countries allow the value of their currency against others in the world to be based on supply and demand. That is, if a lot of investors in other countries buy dollars, then the value of the dollar goes up against other currencies like the Euro or Yen. If a lot of people sell dollars to invest in others, then the value of the dollar goes down.
So when you travel to Canada and they post an "exchange rate", they are telling you how many Canadian Dollars you can get for an American Dollar. That exchange rate will change each day a little bit because both currencies are "free floating".
There is some controversy right now between us and China, because they keep their currency off the float exchange, or at least limited, so that their Yuan is artificially more valuable than it would be in world markets. Obama may have finally just gotten them to relent on this and trade the Yuan more freely. This could lead to lower prices for goods made in the US and sold in China, which may create jobs here in the US.
Exchange rate is the rate applicable for exchanging, or buying and selling one nation's currency with that of another. For example a tourist travelling from India to USA will need to exchange the the money he has in Indian rupees with money in US dollars to be able to buy things in USA. For this at current exchange rates he or she will have to pay approximately 45 Indian Rupees for every US dollar received in exchange.
Countries may decide to have a fixed exchange rates in terms of a fixed amount of gold for which each unit of a national currency can be redeemed from the government. This fixed exchange rate can also be fixed in terms of currency of another country. For example, a few decades back the value of Indian rupee was fixed by government in terms of equivalent US dollars. This exchange rate did not vary from time to time because of market fluctuations in demand for these currencies.
In the system of floating exchange rates, the price of a nation's currency rises and falls in relation to world demand for that currency. However, most governments intervene to prevent too steep fluctuation in their currency exchange rates. A system where this kind of government intervention takes place is often called managed floating exchange rates.