Weak convergence is a concept in probability theory and statistics that describes how a sequence of probability distributions approaches a limiting distribution. Unlike strong convergence, which requires that the distributions converge in a stronger sense, weak convergence focuses on the convergence of the distributions' cumulative distribution functions. This means that for any continuous bounded function, the expected values converge to the expected value under the limiting distribution. In practical terms, weak convergence is often used in the context of Central Limit Theorem, where the distribution of sample means approaches a normal distribution as the sample size increases. It is essential in various fields, including statistical inference and functional analysis, as it helps in understanding the behavior of random variables and their distributions over time.