The denominations (face values) of coins are set by the needs of
business and the prices of goods. This sometimes leads the government
to make some denomination to fulfill a need that disappears as prices
change. One such case was the Two Cent Piece. It was needed for a
short time during and after the American Civil War but that need,
like the coin itself, soon disappeared. It was only made from
1864-73. While a challenge to collect in high grade, it can be fun
and rewarding and a fairly easy series to complete with the exception
of the last year.
Good reference works for those more interested in this type of coin are The Complete Encyclopedia of U.S. and Colonial Coins by Walter Breen or a specialized text such as Longacres Two-cent Piece: 1864 Attribution Guide by Frank Leone.