Derivatives are financial instruments whose price is dependent on the value of some underlying asset or indicator. A stock option is a particular kind of derivative, one that allows the holder to buy or sell stock. All stock options are derivatives, but not all derivatives are stock options.
A derivative is a contract. It's called a "derivative" because the contract's value is derived from the value of something else. A common example is a futures contract for a commodity such as corn. A farmer who wants to lock in a price for his crop might purchase a contract in which he agrees to sell 10,000 bushels of corn for $5 a bushel in October. The contract itself is a security that the farmer can sell to someone else, and the value of the contract depends on the market price for corn. If corn falls below $5 a bushel, obviously, the contract is worth more because the farmer would be getting a premium price for his corn. If corn rises above $5, though, the contract will be worth less.
A stock option is a derivative contract giving you the opportunity to buy or sell shares of stock at a set price -- called the strike price -- at a future date, or within a specified time frame. You aren't obligated to buy or sell any shares; the option merely gives you the right to do so. The value of the option depends on the market price of the stock. Say the option is to buy shares. If the market price is higher than the strike price, the option allows you to buy stock at a discount, so the option's value will rise. If the market price is lower than the strike price, the option's value will shrink.
Varieties of Derivatives
Just about anything can form the basis for a derivative: commodity prices, stock prices, interest rates, cash flows, even news events. If you can find someone else to serve as a counterparty -- that is, take the other end of the deal -- you could set up a derivative based on how much money a given film will earn at the box office or how many days next year there will be rain in Berlin. The price of the derivative will then fluctuate according to the underlying value. Positive reviews for the film or a wet spring in Germany will have an effect on the price.
Varieties of Options
Stock options come in two main flavors: call options and put options. Call options give you the right to buy stock at the strike price. Put options give you the right to sell stock at the strike price. Call and put options both trade on options exchanges, much like stocks themselves, and their prices are continually updating as the underlying stock price rises and falls and as the deadline for exercising the option draws closer.