No need to apologize.
A very short answer to your original question. Assume you have a random variable X and you want to estimate the average of f(X) using Monte Carlo. Then you would oversample X where f(X) is high and undersample where f(X) is low and compensate for the biased sapling by weghts (low for oversample and high for undersample). If done properly, the weighted average has a mean equal to the answer you are looking for, while the standard deviation is reduced in comparison to using unbiased samples.