A Federal Reserve Note is the more technical (and technically correct) name for paper currency issued and used in the United States. They are called such because they are issued on behalf of the US Government by the Federal Reserve Bank.
They are, in a financial sense, IOUs backed by the economy of the contry itself (also known as "fiat money"), not by commodities (as is the case with Silver Certificates and Gold Certificates). In the United States as well as all annexed and protectorate territories they can be used for legal tender -- that is to say they can be used universally in exchange for goods, services and anything else legal in the jurisdiction of the country thereof. Due to the economic strength of the United States, many other countries also allow usage or US Currency within their borders.
The notes themselves are produced by The United States Bureau of Engraving and Printing. Though they are called "paper money", the notes themselves are actually cloth, being made of 75 percent cotton and 25 percent linen. The material also contains red and blue fibers of various lengths that are evenly distributed throughout the paper.
All denominations of notes printed since 1929 (so called "Small size money") are the same size, measuring about 2.61 inches (6.63cm) by 6.14 inches (15.60cm) and are 0.0043 inches thick. Each note, regardless of its denomination, weighs about one gram. Since there are 454 grams in one U.S. pound there should be 454 notes in a pound.
The actual printing is done with a high-pressure Intaglio printing press that actually embeds the ink into the fibers of the note; the inks used are so-called "Patent Green" on the facing side and black on the reverse. Generally speaking, US currency notes will feature portraits of famous US figures (usually political) on the facing side and pictues of famous landmarks (or scenes, as in the case of Two dollar bill) on the reverse -- only portraits of the deceased are allowed. Each note has the denominaltion printed in the corners and is given a unique serial number.