This can be sidestepped if the company only does business in U.S. dollars, but many situations don't allow for that. A higher exchange rate may mean that your company's expenses go up and profit goes down unless the market can absorb a price increase for the product the company sells.
For foreign exchange traders, known as forex traders, the exchange rate is huge. They make currency trades every day based on factors that include exchange rates and their fluctuation.
In a very simple example, if the exchange rate from currency A to currency B is usually around 0.9 and today it's 1.1, a forex trader might take 100 of currency A and trade it for 110 of currency B, knowing that the rate should return to the normal 0.9 soon (barring any global or economic disaster), and they can simply swap their 110 of currency B for 122 of currency A, making a cool 22 units of currency A.
Forex trading is very speculative, though, and you definitely should consider factors beyond the exchange rate when making these decisions.