The phrase The Long Tail (as a proper noun with capitalized letters) was first coined by Chris Anderson in a 2004 article in Wired magazine  to describe certain business and economic models such as Amazon.com or Netflix. The term long tail is also generally used in statistics, often applied in relation to wealth distributions or vocabulary use.
The long tail is the colloquial name for a long-known feature of statistical distributions (Zipf, Power laws, Pareto distributions and/or general Lévy distributions ). The feature is also known as "heavy tails", "power-law tails" or "Pareto tails". Such distributions resemble the accompanying graph.
In these distributions a high-frequency or high-amplitude population is followed by a low-frequency or low-amplitude population which gradually "tails off". In many cases the infrequent or low-amplitude events—the long tail, represented here by the yellow portion of the graph— can cumulatively outnumber or outweigh the initial portion of the graph, such that in aggregate they comprise the majority.
Such distributions are surprisingly common. In standard English, the word "the" is the most common word and other short words such as "of", "is" and "have" are also quite common. These common words are vastly more common than most other words. For example, about 12% of all words are "the" (while "barracks" occurs less than 1 out of 50,000 words), but cumulatively, words roughly as rare as "barracks" make up about a third of all text. These rare words are the long tail in English vocabulary.