One has to realize that a Monte Carlo simulation is an integration tool. Suppose you have a curve in an xy plot, y=f(x). If you throw random (x,y) pairs in the square containing the f(x) and count the number where y is less than f(x) versus the number y larger than f(x) you get an estimate of the area under f(x), i.e. the integral of the function.
In elementary particle physics, the phase space ( equivalent to the square in the simple example) is known. Theoretical functions are used as a weight to a random number generator, to generate "events" according to their parameters and checked against the real event data. If the fit is bad, the parameters are changed to improve it.
The advantage is
a)Detector limitations can be programmed in the phase space and events generated with the limits of the detector included
2) The method is much more efficient in computer time than the numerical integrations necessary over the innumerable functions entering the problems, detector and theory.
3) Once a Monte Carlo event sample is generated it can be used "as if it is data" over and over again to get plots not thought up beforehand.
In the recent LHC experiments the Monte Carlo events were generated way before the real data, according to the detector limitations and to the theoretical expectations from the Standard Model. The existence of these Monte Carlo data set allowed fast checks on whether new physics is appearing. New physics will appear as statistically significant deviations from the Monte Carlo curves.