Simulation-based valuation in a nutshell

Explain what Monte Carlo simulation is in the context of quantitative finance.

It estimates an expectation by averaging over many randomly simulated scenarios. For pricing, you simulate the underlying's paths under the risk-neutral measure, compute the payoff on each, average and discount. It copes easily with many underlyings and path-dependent payoffs, but its error shrinks only like $1/\sqrt n$, so variance reduction and quasi-random numbers are used; it is also central to risk measurement such as VaR.