CLT (Central Limit Theorem)

A theorem on which most statistical tests are based that states that the means of random samples from any distribution (normal or non-normal) with a mean of μ and a variance of σ² will have the following attributes: 1) an approximately normal distribution, 2) a mean equal to μ, and 3) a variance equal to σ²/n. What does this mean? As an example, suppose you roll a pair of dice 10 times and write down the average of all the rolls and repeat that process 10 more times; after doing so you will find that 1) the averages of each of those sets of rolls will be about the same, and 2) the more you roll, the variance between the values will become more and more narrow (i.e., less variation).
Related StatStuff Video: 
   -Section 6-Analyze Phase, Lesson #11 - Hypothesis Testing: Statistical Laws and Confidence Intervals