What is a Federal Reserve Note?
A Federal Reserve note is the formal name of U.S. currency.
How Does a Federal Reserve Note Work?
Founded in 1862, the U.S. Bureau of Engraving and Printing creates and produces Federal Reserve notes. It does not produce coins (that's the job of the United States Mint).
The production of Federal Reserve notes includes creating the templates and materials necessary to print currency. Because currency is a printed item, the U.S. Bureau of Engraving and Printing also must detect and deter counterfeit currency (in conjunction with the U.S. Secret Service).
Why Does a Federal Reserve Note Matter?
The U.S. Bureau of Engraving and Printing is the United States' only source of Federal Reserve notes. It has production facilities in Fort Worth, Texas, and Washington, D.C. It is also the largest producer of government security documents in the United States.
Most currency only has value because people want it. This idea is what made beaver pelts, shells, peppercorns, tulip bulbs, and other things into currency at various points in history. However, when the demand (or fashion) faded for some of these goods (or more people found they really needed corn instead of beaver pelts), these systems became cumbersome. Paper currency solves these problem because it is exchangeable for any good or service that people want (rather than just beaver pelts).
This isn't to say that paper and coins aren't the only forms of viable currency today. Quite often, companies use shares of their own stock as currency to acquire other companies, and anybody who has ever watched a crime show knows that cigarettes can buy a lot in prison.