An option to buy something else is called a call option; an option to sell something else is called a put option. An option has a strike price, which is the price at which you are entitled to buy (or sell) the underlying commodity, or stock, or foreign currency, or whatever.
Options allow the owner to speculate in the possibility that market prices will change in a certain direction, without actually spending the value of the underlying item. For example, suppose WTI crude is $85.75/bbl. In order to make $1000 off of a $0.25 increase in the price, you ordinarily would need to own 4000 bbls of crude, which you can't afford. So, instead, you buy a call option for 4000 bbls with a strike price of $85.75/bbl (i.e., exactly what it is now). This option will cost a tiny amount of money. If the price goes up to $86.00/bbl, you don't own the oil, but your options are now worth $1000 to somebody who wants to buy that oil.
An option with intrinsic value (for example,a call option whose strike price is less than the spot price) is "in the money." An option with no intrinsic value is "out of the money."
ANNA: For most people. But if you're already in the business of buying or selling a particular thing, an option can protect you against a bad price movement.
BILL: But options on stocks? I mean, unless a company wants to reward its own executives, or something?
ANNA: Well, you might need options on stocks to hedge risk, if you're a fund manager. That way you can focus on long-run investing.
* Can be derogatory when used in the right context.
Male B : Word up man! Every 5 one of them's a banging chick.
Female A : Wow, look at Johnny over there, isn't he just dreamy? 8)
Female B : Oh please Bertha, your not even an option for him. >_>
Female A : OH HELLZ NO, you did not just say that!