Derivatives are financial instruments whose value is derived from the value of something else. They generally take the form of contracts under which the parties agree to payments between them based upon the value of an underlying asset or other data at a particular point in time. The main types of derivatives are futures, forwards, options and swaps.
If you think oil is going to cost $100/barrel a year from now, you can buy a tanker full of oil and wait to cash in. Obviously if it costs $200/barrel you win big, and if it's $2/barrel (because aliens have arrived with a miraculous new power source) you're left with a tanker that no one wants and a stupid look on your face.
This is - often incovenient. So it's simpler to bet on the future value of something without having to buy any of it. You make an agreement with someone else who - say - thinks it's going to cost $50/barrel a year from now. When the time is up you work out who owes what to whom, based on what the oil would have been worth if you'd bothered to buy it, and off you both go.
Occasionally there may even be some relationship to real oil involved in this process - e.g. if you run a plastics plant and need to buy the oil at a good price. Some derivatives are based on real stuff moving around.
But if you can find someone willing to bet against you, you can just as well ignore the oil and bet only on its price.
Bizarre? For sure. But you can trade in the price of anything - include abstract things like the FT and Dow indices. And the weather.
The advantage is that you need much less money up front to win big, because you don't need to buy a tanker full of oil/soft toys/gold/dollar notes to profit from a change in prices. All you need is someone willing to bet against you.
'Anything' means literally anything you can persuade someone to take a bet on. The derivatives markets include standard bets on future stock prices, individually or in groups, and commodities like gold and oil, currencies, and so on.
Also, the bets don't have to assume that prices will rise. You can also bet that prices will fall. (Obviously, if everyone agreed on which direction prices would move in, there would be no excitement risk and therefore no profit.)
You can also bet on the future value of loans. (And - so far as I know - on the future value of certain bets.) E.g. with mortgages, there's a risk that some people will default. But as long as that number is low enough, lending money for mortgages is still profitable.
You can bet on how true that is by betting on the future value of the stocks of the companies that have made those loans. You can also buy parts of the loans - which is like buying oil. And also bet against future value without buying the loan, by betting on the value of packaged deals of loan-related financial thingummies which come in a plain brown wrapper with instructions that you're not supposed to read.
Now, some unscrupulous people have been suggesting that with these financial bets and loans, the risks have been disguised so that people don't really know what they're betting on. They think they're betting on a sure thing, but in fact they're betting on a horse with three legs and a missing ear.
So it goes. People may not always be honest with you, even when they have a legal obligation to be. And since you're probably not in the loop unless you know all the players personally, you need nerves of steel and plenty of spare cash - or inside information - to play with derivatives profitably.
The one sentence answer is that derivatives are a bet on the future value of something.
Now that is an easy to understand definition and makes understanding the other explanations easier too. Thanks!