A "power law distribution" refers to a probability distribution of a certain mathematical form, usually describing "...phenomena where large events are rare, but small ones quite common. For example, 

* There are few large earthquakes but many small ones. 
* There are a few mega-cities, but many small towns. 
* There are few words, such as 'and' and 'the' that occur very frequently, but many which occur rarely. [http://ginger.hpl.hp.com/shl/papers/ranking/ranking.html]. 

One mechanism which can explain a PowerLaw distribution in domains of social popularity is PreferentialAttachment. In this domain, a popular PowerLaw is called the LongTail, which typically follows ZipfsLaw.