This only applies for independent and identically distributed (iid) variables - or ones that are approximately so, and is the result of the Central Limit Theorem of statistics
…. According to it the mean of any set of iid variables is distributed as an approximate Gaussian distribution, with the same mean as the underlying data and a standard error which is proportional to 1/sqrt(n) where n is the number of observations. So, as the number of observations increases, the standard error of the estimated mean value of the variable decreases. Decreased variability = increased accuracy. (MORE) 
