Monte Carlo Simulation is simply the calculation of a model many times using an automated process that randomly samples the possible values for the model’s inputs. The output of a simulation will therefore indicate the likelihood of any possible value (or range of values). In principle (for the true likelihood of any output value to be determined), the random samples used for each input are drawn from a process (distribution) which corresponds to the true nature of the risk (or uncertainty) of that input.
The first intensive use of MCS was in the 1940s by scientists working on nuclear weapons projects at the Los Alamos National Laboratory. There is was simply used as a numerical method to evaluate complex integrals: The value of the integral of a function is equal to the average value of the function over an interval multiplied by the length of the interval. Thus, by calculating the value of a function at various random points in the interval and calculating the average of these, the integral can be estimated.
In business applications, MCS can be used to assess the risk in projects or business cases, and to value or evaluate businesses or financial products and contingent contracts. The value of the information depends on the quality of the underlying risk model.
Note the one should not confuse the risk modelling process with the simulation – the latter simply calculates the many possible outputs of the risk model, whereas the risk modelling process requires risk identification/mapping/quantification etc. When correctly used, the risk modelling/simulation combination should provide insight, as well as support a decision process (e.g. by helping to assess likelihoods of outcomes), albeit one who ultimate use is also dependent on the risk-tolerance of decision-makers (and is therefore in general beyond the scope of the model or of objective analysis). Of course, risk modelling/simulation can be incorrectly implemented (whether intentionally or not) and then may (intentionally or not) be used to justify incorrect decisions (e.g. those which in reality exceed the appropriate level of risk to take, even if this has been hidden or has not been made explicit).
My book Business Risk and Simulation Modelling covers these topics in much more detail.