In the Monte Carlo method, the standard error of the price estimate is the standard deviation of the discounted payoffs on the paths divided by the square root of the number of paths. When the number of samples is large, the range from the estimate minus 1.96 standard errors to the estimate plus 1.96 standard errors contains the true value (the expected value) about 95% of the time.
Consider a hypothetical example in which the standard deviation of the values on the paths is 13.4. The standard error with 10,000 paths is 13.4 ÷ 100 = 0.134. Quadrupling the paths to 40,000 halves the standard error to 0.067.