Observe a random variable X very many times. In the long run, the proportion of outcomes taking any value gets close to the probability of that value. The Law of Large Numbers says that the average of the observed values gets close to the mean μX of X. In this applet, we represent a random variable X as the total number of spots on the "up" faces of one or more dice.
This site provides a simulation of the law of large numbers. The site also provides a visualization along with the simulation.