In doing a bit of research for my collaboration with Halcyon Days (the decorative giftware company) I came across the legend behind the phrase.

The Halcyon bird is a character in Greek mythology. The phrase comes from the ancient belief that the Halcyon calmed the surface of the sea in order to brood her eggs on a floating nest for fourteen days. This resulted in fourteen days of calm weather, to be expected around the winter solstice. 

The belief in the bird’s power comes from the story of Aeolus, the ruler of the winds, and his daughter Alcyone, who was married to Ceyx, the king of Thessaly. Ceyx was drowned at sea and Alcyone threw herself into the sea in grief. Instead of drowning, she was carried to her husband by the wind.

The legendary Halcyon bird is usually identified with the kingfisher because it also nests on the sea around the time of the winter solstice.

In mediaeval times it was also thought that if the dried carcase of a kingfisher was hung up it would always point its beak in the direction of the wind.