Barrier options are extensions of standard stock options. Standard calls and puts have payoffs that dependon one market level: the strike. Barrier options have payoffs that depend on two market levels: the strike and the barrier.
Ins and Outs of Barriers Part 1
Part 2, expands on this presentation. Somewhat more more exotic barrier options are explored, and a summary of the mathematical theory behind the valuations is present.
Ins and Outs of Barriers Part 2