The Central Limit Theorem says that the average of a large enough sample is normally distributed around the true population average, regardless of the shape of the underlying data. This is the engine behind statistical inference: it lets us attach probabilities to how far a sample is likely to stray from reality, which is what makes polling, hypothesis testing, and confidence intervals work.
Related: Know the bell curve intimately enough to know where it fails · Mediocristan is tyranny of the collective, Extremistan of the singular