I heard two different answers to that question:
The first answer is that while an animal's head is located on one of its body's ends, the tail is located on the opposite side. Therefore, "head" and "tail" represent the two opposite sides of an object.
The second answer, for which I couldn't find corroboration, is that old English coins had, on the side opposite to the side on which a portrait was engraved, the figure of St. George and the dragon. The dragon, being, ultimately, just a big lizard with wings, had a tail, and the nickname "tails" was given to this side of the coin.