Asymptotic normality refers to the property of a sequence of random variables that, as the sample size increases, their distribution approaches a normal distribution. This concept is crucial in statistics, particularly in the context of the Central Limit Theorem, which states that the sum or average of a large number of independent, identically distributed random variables will tend to be normally distributed, regardless of the original distribution. In practical terms, this means that for large samples, we can use the normal distribution to make inferences about the population from which the sample is drawn. This simplifies analysis and hypothesis testing, allowing statisticians to apply techniques that assume normality even when the underlying data may not be normally distributed.