A type of exotic option, the value of which depends on the underlying passing (or not) a particular price point.
Knock-out and knock-in options are the commonest types of barrier option.
Knock out options
A knock-out option is cancelled if the price passes a particular level. Once the price barrier has been breached, the option cannot be exercised regardless of what subsequently happens to the price of the underlying
A knock-in option can only be exercised if the price has passed (above or below, depending on the option) a certain level over the life of the option. Once the barrier is breached the option may then be exercised regardless of what the price does subsequently.
Problems with barrier options
Like all exotic options, barrier options are much harder to price than vanilla options, and no type of option is entirely easy to price despite the existence of well established formulae such as Black-Scholes.
Knock-out options are fairly popular because are often much cheaper then vanilla options. However, the reason they are cheaper is that they exclude extreme outcomes, when value of the option is greatest: i.e. when the option very deeply in the money. These outcomes may be unlikely (if the barrier is sufficiently high or low), but because security price distributions are often fat tailed they tend to be more likely than investors expect.