What are financial derivatives and how do they work?

I need to know this for a school assignment and I am not planning on going into anything business related so I have no idea what they are. I have searched online but I am not getting a very clear answer. If anyone could help me this would be greatly appreciated.

Consider this:

They are contracts between two parties where the value of the contract is contingent upon the future value of certain assets. For example, if I approach a farmer to buy next year's crop of corn for $1 million, then we have a derivative. Here's why:

1. The farmer may not be able to produce a crop next year. (I lose.)
2. The market price of next year's crop when it is harvested is worth $1.5 million (I win).

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Derivatives include contracts to buy or sell something for future delivery (forward and futures contracts), contracts involving an option to buy or sell something at a fixed price in the future. (options) and contracts to exchange one cash flow for another (swaps), along with simple combinations of forward, futures and options contracts. (Futures contracts are similar to forward contracts, but they are standardized contracts that trade on exchanges.)
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Derivatives mean investment vehicles. You now can figure out the rest.

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