These terms have their roots in Roman coins which included the head of the ruler or emperor on one side, a practice still common in many countries of the world today. In Britain coins have long had a head of the ruling monarch on one side and another image on the other. The correct term for the side of a coin with the head on it is the ‘obverse’ side, whilst the other side is called the ‘reverse’. When flipping a coin, though, they are more commonly known as ‘head’ and ‘tail’. ‘Tail’ probably comes from the fact that the head is the top of your body and the extreme opposite of that would be the tip of your tail – if you had one.
Today some countries have coins which neither have head nor tail, but the terms have stuck.