Most coins have a side where the imprint of a person, such as a current or former head of state, is impressed — this side is called the "Head" side (since the embossing is of the head of a person). The other side may have any imprint, or none, and is called the "Tail" side.
In 1870 Brewer's Dictionary of Phrase and Fable describes heads in a similar way and details tails as being the opposite and obvious reverse to heads. The expresssion 'can't make head nor tail of it' expresses this concept of opposites.
Generally, one person throws the coin up in the air, and the second person must predict which side of the coin will lay face up after it rests back on the ground. A correct prediction results in a win. Another variation has the person catch the coin in one hand and slap it on the back of their other hand. Traditionally, the second person calls out "heads" or "tails" while the coin is in the air.
The Australian game of Two-up is closely related, and involves traditionally two half-pennies. Coin flipping as a game was known to the Romans as "navia aut caput" (ship or head), as some coins had a ship on one side and the head of the emperor on the other.
A related game, Cross and Pile, was played in England for many centuries. The cross was the major design element on one side of many coins, and the Pile was the bottom part of the die used to cast the other side of the coin. Cross and Pile is derived from the Greek pastime called Ostrakinda, played by the boys of ancient Greece. Having procured a shell, they smeared it over with pitch on one side and left the other side white. A boy tossed up this shell, and his antagonist called white or black (In the Greek, nux kai hemera, that is, 'night or day') as he thought proper, and his success was determined by the white or black part of the shell being uppermost.
In Italy this game is called Testa o croce ("head or cross"). In Germany the game is called Kopf oder Zahl ("head or number", because the other side shows the coin's value). In Ireland it is usually called Heads or Harps, since the obverse side of Irish coins (both Euro and the former currency, the Irish punt) always shows a harp. In Brazil, it is called Cara ou Coroa ("face or crown"). On Brazilian coins, one of the sides are called Cara(marked with a face); the other side is called Coroa(crown, or another symbol). In Mexico it is called Aguila o Sol (Eagle or Sun). In Russia it is called Орёл или ре́шка (Oryól ili réshka - eagle, or another symbol). In Hong Kong, it is called 公定字 ("Head or word"). On Hong Kong coins, the obverse side of the coin is basically words that said the amount of the coin. The reverse side, however, is flower. Although the reverse side is not a head anymore, Hong Kong citizens still use that term to call the game.