Its central insight is that an asset should be judged by what it does to the portfolio, not in isolation. A volatile asset that is uncorrelated with everything else can reduce total risk even while raising the risk of the position that holds it.
The mathematics uses variance as the definition of risk and assumes returns are well described by means, variances and correlations. That is a workable approximation in calm periods and a poor one in crises, when correlations rise, distributions develop fat tails, and liquidity disappears.
Use the intuition and be sceptical of the precision. Combining genuinely different return drivers helps; believing an optimiser's third decimal place does not. See efficient-frontier, tail-risk and capital-asset-pricing-model.
Related: efficient-frontier, capital-asset-pricing-model, mean-variance-optimization, correlation, tail-risk