The Central Limit Theorem ensures that the distribution of a sampling statistic (like a mean) is approximately normally distributed if your sample size is large enough (typically #> 30# when estimating a mean), regardless of the shape of a population distribution.

This is of tremendous practical value when you wish to estimate a population statistic: you can just take one sample, and then use the theoretical distribution for the sampling statistic to estimate its uncertainty. In practice, there is thus no need to take multiple samples.