As a noun, a halcyon is a kingfisher, or at least a bird which we have associated with the kingfisher. It is part of a Greek legend in which it calmed the sea.
As an adjective, halcyon describes something or someone to be joyful, peaceful, or prosperous. The most common use is to describe a period of time as the halcyon days, which is a reference to the myth.
According to the Greeks, the Halcyon days come every January. The seas would be calm so that the kingfisher’s eggs were protected while they incubated in the nest. Incidentally, in the myth Halcyon was originally a goddess and was transformed into a bird after she tried to commit suicide. As a bird she was reunited with her lover, who was also made into a bird. So some Greek myths do end happily.
Side note: the term is pronounced \ˈhal-sē-ən\ (hal see in).
The halcyon era of Port Talbot’s steel industry, however, proved short-lived. [Wales Online]
Remember those halcyon days before two nurses in Dallas contracted Ebola from Liberian Thomas Eric Duncan? People were alarmed but not panicked, experts assumed that certainly the average tertiary care hospital in the U.S. could handle Ebola patients, and people thought it was ridiculous to think about things like cleaning elevators after an Ebola patient had ridden in one. [Huffington Post]
The brother and sister, who took up Kennedy membership this year, have been Hawks fans since childhood, when the halcyon years and players like Brereton, Dunstall and Platten drew their attention. [Wangaratta Chronicle]
What a halcyon thought: that large companies and SME’s within the Eurozone would like to borrow money so they can expand their companies in order to make more money. [Forbes]