What is Herfindahl-Hirschman index in Economics?

A measure of the degree to which production in a market is either concentrated or dispersed. A market in which production is divided among several producers is considered to be less concentrated than one in which all production is in the hands of just one producer. The Herfindahl-Hirschman index is used by anti-trust agencies which possess the mandate to promote competition. It is calculated by squaring the market share of each producer in the market and then comparing the sum to a scale. Critics of the idea say that the lack of legal barriers to entry is a better measure to gauge competition in any market.