Question: How would you describe the **Power Law** in simple words? The Wikipedia entry is too long and verbose. I would like to understand the concept of the power law and how and why it shows up everywhere.

For example, a recent Economist article **[Cry havoc! And let slip the maths of war](http://www.economist.com/node/18483411)**, shows that terrorist attacks follow an inverted power law curve.

Answer: 
Just to expand on Ross Millikan's answer. Power-laws are important and pop up all the time because they obey [scale-invariance](http://en.wikipedia.org/wiki/Scale_invariance). Scale-invariance is the property that a system behaves the same when all length-scales are multiplied with a common factor. System show scale invariance if there is no characteristic length scale associated which, e.g., happens at phase transitions.
An easy to read article with data: <http://www.jmir.org/2015/6/e160/>