Before defining central limit theorem let's clarify the term i.i.d.
independent and identically distributed (i.i.d) random variables - this means that the random variables we consider have the same probability distribution as the others and they are mutually independent. An example would be two dice experiments performed simultaneously.
Central limit theorem states that if you take the average of the outcomes of sufficiently large i.i.d random variables, with finite mean and variance, it follows a normal or Gaussian distribution.
Here is an example. Suppose we throw a dice 10000 times. Then the outcome would more or less look like this (uniform distribution).
Now, let's throw 2 dices together 10000 times and observe the average (or you can observe the sum of the outcomes for that matter) of outcomes.
Now, you get the idea. Suppose we throw 50 dices together 10000 times and observe the average (or sum) of outcomes.
This looks like a normal distribution to me.
Wikipaedia says: "Since real-world quantities are often the balanced sum of many unobserved random events, this theorem provides a partial explanation for the prevalence of the normal probability distribution".
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