Specify a process for each risk factor - volatilities, correlations, distribution shape - generate ten or a hundred thousand paths, revalue the portfolio in each, and take the percentile. Unlike the parametric method it can handle options, path dependence and non-normal inputs.
Its flexibility is exactly its exposure. The output is a precise-looking distribution generated entirely by the assumptions you supplied; feed it normal returns and stable correlations and it will confidently reproduce the same understatement as parametric-var with more decimal places and more compute. Garbage in, beautifully rendered garbage out.
Where it earns its keep is in showing sensitivity. Run it with correlations at their trailing average and again at 0.9, or with volatility doubled, and the spread between outputs tells you more about your risk than any single number does. That is really scenario-analysis wearing a simulation costume, and it is the honest use of the tool.
Related: value-at-risk, scenario-analysis, monte-carlo-reshuffle, parametric-var