Wat is Monte Carlo method, variance reduction?

The Monte Carlo method estimates $\mu = \E[f(X)]$ by the average $\hat\mu_n = \frac1n\sum_{i=1}^nf(X_i)$ of independent draws. Variance reduction is any change of estimator that keeps $\E[\hat\mu_n] = \mu$ (or makes the bias negligible) and lowers its variance at equal cost.