Monte Carlo methods are stochastic (probabilistic) systems that use many random samples to derive properties of a complex system.
Monte Carlo methods are stochastic methods that use large sample sizes to gather information about a complex system. The outcomes of these trials can then be used to draw generalizations about the system as a whole, without first needing a proper solution.
Monte Carlo methods are especially useful when a numeric solution is available, but which is too complex to solve for directly. They are general enough that their use is widespread; Wikipedia provides a list too exhaustive to reproduce here.