Can anyone give an example of a workplace or an area where some risk could be mitigated by using a derivative?

In finance, a derivative is a security whose price is dependent upon or derived from one or more underlying assets. The derivative itself is merely a contract between two or more parties. Its value is determined by fluctuations in the underlying asset. The most common underlying assets include stocks, bonds, commodities, currencies, interest rates and market indexes. Most derivatives are characterized by high leverage.

Futures contracts, forward contracts, options and swaps are the most common types of derivatives. Because derivatives are just contracts, just about anything can be used as an underlying asset. There are even derivatives based on weather data, such as the amount of rain or the number of sunny days in a particular region.

Derivatives are generally used to hedge risk, but can also be used for speculative purposes. For example, a European investor purchasing shares of an American company off of an American exchange (using American dollars to do so) would be exposed to exchange-rate risk while holding that stock. To hedge this risk, the investor could purchase currency futures to lock in a specified exchange rate for the future stock sale and currency conversion back into euros.

Exchange rate and interest rate risks are managed with a variety of straightforward techniques, including match funding and selective use of derivatives. We use derivatives to mitigate or eliminate certain financial and market risks because we conduct business in diverse markets around the world and local funding is not always efficient. In addition, we use derivatives to adjust the debt we are issuing to match the fixed or floating nature of the assets we are acquiring. We apply strict policies to manage each of these risks, including prohibitions on derivatives trading, derivatives market-making or other speculative activities.

The notes AICPA's Common Sense Questions About Derivatives is useful reading (3rd link)