Halcyon comes from alcyon, a bird in Greek legend commonly considered to be the kingfisher. The h was tacked onto alcyon because of the association with the sea, which is hals in Greek.
Aeolus was the ruler of the winds. He had a daughter Alcyone who was married to the king of Thessaly, Ceyx. Ceyx drowned at sea and in her grief, Alcyone threw herself into the sea. Her father, the ruler of the winds, instead carried her to her husband. The gods changed them into winter birds. Around the winter solstice, the ocean calms and for fourteen days, Alcyone will sit on her floating nest out at sea and hatch out more little kingfishers.
Halcyon means calm and tranquil, happy and carefree; but it is rarely used outside the phrase halcyon days. Halcyon days, those 14 days that the weather is calm around the winter solstice. Seven days before and seven after.
The winter solstice was December 22 this year, so we still have a few halcyon days left. One more halcyon day until Christmas!