The easiest way to see it is when you're making a cake, or whipping cream. A single band forms around the middle of the bowl, with fewer and fewer specs out from the middle. If you were to plot the distribution of these points you would get something like this
This is called the Normal Distribution. This is what "normally" happens. Most things are around some central value, but everything is possible, it's just less and less likely the further you get from the middle. That's why there's whipped cream on your fridge. If you run the beeters for long enough, the one in a million chance can happen, and that rare value way off on the curve is far enough out to leave the bowl and go wizzing across the room to hit your fridge.This is the basis of a large part of statistics. As you can see the probability drops of very quickly. Something called the Empirical rule tells us that we should expect almost 70% of the values within one standard deviation, and a whopping 95% within 2 standard deviations. By the time we get 3 standard deviations out we covered 99.6% of all possible outcomes from the population.
This is how so called anomalies occur. The bulk of observations are pretty close to the middle, occasionally there are some that are slightly off the mean, but once in a blue moon (That's two moons in one month btw) truly crazy stuff happens. We call those outliers.
And although the formula for it is rather unpleasant you'll notice that both pi and e (a number like pi) and the square root of two are all part of it. For math types, this is deep. Potentially the three most impotant numbers in science all part of a formula that came out of everyday experience. Pretty awesome. So the next time something truly incredible and strange happens, just remember it's "normal".
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