A Monte Carlo model, in its most general description, includes any method of estimating a value by the random generation of numbers and statistical principles. As a way of pricing or valuing options, Monte Carlo option models use a pseudo-random sequence, one that will be random enough to simulate a range of outcomes yet deterministic enough to reproduce when necessary. (If the number generation is truly random — pegged, for instance, to background cosmic radiation, it will produce a sequence of less utility because it will be impossible to replicate.)
Monte Carlo models are particularly useful in the valuation of options with complicated features that make them difficult to value through a straightforward Black-Scholes style computation. Asian options are an example.
Some trace the historical development of such models to the 18th century French naturalist Buffon, and a question he asked about the results of dropping a needle randomly on a striped floor or table. See Buffon's needle.
There's been a number of recent advances in the field, i.e. Markov chain Monte Carlo methods, which make use of samples that are neither identically nor independently distributed.
Don L. McLeish, Monte Carlo Simulation & Finance (2005) ISBN 139780471677789