A digital option is a financial instrument that either pays off at a specific quantity or not at all. If the asset underlying the option crosses a certain threshold of value, the option yields a specific amount of money. If the asset does not cross the threshold, the option becomes worthless. Digital options are also known as binary options and all-or-nothing options; they classified as 'exotic' options despite their relative simplicity.
A normal stock option is the right to buy or sell an asset at a certain price at or before a certain time. The price is called the strike price, and the date is called the expiration date; an option to buy is called a call option and an option to sell is called a put option. If the underlying asset's price never moves past the strike price, normal options and digital options function the same way: they aren't worth the paper they're printed on.
The difference between a digital option and a normal option is that the digital option pays off the same amount regardless of how far above the strike price its underlying asset rises—or, in the case of a put option, regardless of how far it falls. A normal call option becomes massively valuable if the underlying asset becomes ten times more expensive. For a digital option, it makes no difference whether or not the asset's value rises a penny or a dollar above the strike price. The value of digital options relative to normal options thus reflects a market's assessment of its own volatility skew.
There are actually two significantly different categories of digital option. All options come in these categories, but the choice of category makes an especially large difference in this case. American-style options are more flexible, as there is no set time that they must be exercised; any time before the expiration date is possible. European-style options must be exercised precisely at the expiration date. This means that American-style digital options pay off as soon as the asset crosses the strike price, whereas European-style digital options only pay off if the asset is above that price at a previously specified time. Most digital options are European-style.
Digital options can also be structured to pay out either cash or assets. That is, if the price of the asset in a digital call option exceeds a certain price, the owner of the option can receive either a fixed amount of cash or a fixed quantity of the asset. These types are given the fitting names cash-or-nothing and asset-or-nothing.