Law
Given large enough samples, the distributions of the sample means are all normal, regardless of whether they came from a normal, uniform or exponential distribution.
Simply:
Imagine a funky dice that unfairly favours the odd numbers. If you were to take 1,000 samples of 10 dice throws and plot the means of each, it would look strikingly like normal distribution, even though it did not originally come from a normal distribution.
Standard Error of the Mean:
Also known as the standard deviation of the mean, \sigma^{2}_\bar{X}