The intuition behind that technique, when applied to derivatives, is the following: note that the source of the variance of a derivative will be directly dependent on the risks (e.g. delta, vega) of this derivative. This is because any error on, say, the estimator for the forward value of an underlier, will generate a corresponding error depending on the delta of the derivative with respect to this forward value. The simplest example to demonstrate this consists in comparing the error when pricing an at-the-money call and an at-the-money straddle (i.e. call+put), which has a much lower delta.