A Barrier option becomes active or inactive when a pre-set price barrier is breached. For example an "up-and-in" call option would only be active if at some point during the option's life the price of the underlying exceeded the barrier, if it failed to do so it could not be exercised regardless of whether it finished in-the-money or not. Similary a "down-and-out" put option would be automatically cancelled if, during the option's, life the underlying asset's price fell below the barrier.
Double barrier options have two barriers, one above the spot price (ie the market price of the asset at the start of the option's term) and one below the spot.
Barrier options are always less expensive than equivalent European/American options as there is always a probability that the options will be knocked out or not be knocked in. The only input in addition to the black scholes inputs is barrier level and the barrier type (ie knock in or knock out).
Barrier options cannot be valued using a Black Scholes model and are typically valued using a monte-carlo or binomial option pricing model
DerivativeOne features a free valuation tool for pricing a single and double Barrier Options on Stocks, Currencies, Commodities and Futures