Derivatives are a type of financial instruments or securities that do not have any value on their own. Their value comes from (is derived from) the value of some other thing. The derivatives market is the market in which people buy and sell derivatives.
Derivatives do not include things like stocks in companies, barrels of oil, or mortgages on houses. These things have value on their own. Instead, derivatives are securities that are based on those types of things that have inherent value. One example of a derivative would be a futures contract. Imagine that you and I agree on a futures contract in oil. Our contract specifies that I will deliver a certain amount of oil to you on a specific date that is relatively far in the future. It says how much you will pay for the oil on that date. In general, I am betting that the price of oil will drop between now and then while you are betting that it will go up. That futures contract is a derivative. It has value because it is worth (depending on what you think the price of oil will do) the opportunity to buy the oil at the specified price or the opportunity to sell the oil at that price. However, its value is based on the value of the oil itself, not on the inherent value of the contract.
The derivatives market is the market in which people buy and sell these financial instruments. You might, for example, decide that you made a bad deal or you might simply want to make some cash now and so you decide to sell the contract to someone else. They will buy because they believe that the price of oil will go up in the future. People can and do buy and sell these types of contracts all the time. These transactions make up the derivatives market.
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