Convergence in Distribution, also known as weak convergence, refers to a situation in probability theory where a sequence of random variables approaches a limiting distribution. Specifically, if the cumulative distribution functions (CDFs) of the random variables converge to the CDF of a limiting random variable at all points where the limiting CDF is continuous, then the sequence is said to converge in distribution. This concept is important in statistics and is often used in the context of the Central Limit Theorem, which states that the sum of a large number of independent random variables will tend to follow a normal distribution, regardless of the original distributions of the variables. Convergence in distribution helps in understanding the behavior of estimators and test statistics in asymptotic theory.