When we first encounter asymptotic (large sample) theory in econometrics, one of the most important results that we learn about is the Central Limit Theorem. Loosely speaking we learn that if we aggregate together enough values that are sampled randomly from the same distribution, with a finite mean and variance, then this aggregate starts to behave as if it is normally distributed.
However, too few courses make it clear that this "classical" central limit theorem is just one of several such results. The one that assumes independently and identically distributed values is actually the Lindeberg-Lévy Central Limit Theorem. There are other, related, results that deal with less restrictive situations.