In general, banknotes of a value less than one of the issuing authority's standard units. When talking about U. S. paper money, this term refers to the less than a dollar denominated, government-issued notes from 1862 to 1876.
Fractional Currency is paper notes issued by the United States Treasury Department in the 1870s in 3 cent, 5 cent, 10 cent, 15 cent, 25 cent and 50 cent denominations. See pictures of each of these denominations at http://en.wikipedia.org/wiki/Treasury_%28Coin%29_Note. These notes are also referred to as "Treasury (Coin) Note" in Wikipedia, with the description United States Treasury Notes were maturity based printed money popular during the late 19th and early 20th centuries.