The Gnedenko theorem is a result in probability theory that deals with the asymptotic behavior of the maximum of a sequence of independent and identically distributed random variables. It states that under certain conditions, the distribution of the normalized maximum converges to one of three types of extreme value distributions, known as Gumbel, Fréchet, or Weibull distributions. This theorem is significant in fields such as statistics and risk management, as it helps in understanding the behavior of extreme events, like floods or stock market crashes. By applying the Gnedenko theorem, researchers can better predict the likelihood of rare occurrences based on observed data.