The "Killing of the Divine King" is a motif traced by Sir James Frazer in his work anthropological work The Golden Bough, and which subsequently became immensely influential in fantasy fiction. The relevant bit of text:

There is some reason to think that in early times Adonis was sometimes personated by a living man who died a violent death in the character of the god. Further, there is evidence which goes to show that among the agricultural peoples of the Eastern Mediterranean, the corn-spirit, by whatever name he was known, was often represented, year by year, by human victims slain on the harvest-field. If that was so, it seems likely that the propitiation of the corn-spirit would tend to fuse to some extent with the worship of the dead. For the spirits of these victims might be thought to return to life in the ears which they had fattened with their blood, and to die a second death at the reaping of the corn. Now the ghosts of those who have perished by violence are surly and apt to wreak their vengeance on their slayers whenever an opportunity offers. Hence the attempt to appease the souls of the slaughtered victims would naturally blend, at least in the popular conception, with the attempt to pacify the slain corn-spirit. And as the dead came back in the sprouting corn, so they might be thought to return in the spring flowers, waked from their long sleep by the soft vernal airs. They had been laid to their rest under the sod. What more natural than to imagine that the violets and the hyacinths, the roses and the anemones, sprang from their dust, were empurpled or incarnadined by their blood, and contained some portion of their spirit?

The motifs and ideas that Frazer put forward in his book drew upon interpretations of many different cultures, aiming either to find a euhemeristic survival behind pretty much any ritual, holiday, or tradition. The problem is, the historical evidence for some of these behaviors doesn't always support his interpretation. For example, one example he cites of a "king for a day" celebration:

A custom of annually appointing a mock king for a single day was observed at Lostwithiel in Cornwall down to the sixteenth century. On “little Easter Sunday” the freeholders of the town and manor assembled together, either in person or by their deputies, and one among them, as it fell to his lot by turn, gaily attired and gallantly mounted, with a crown on his head, a sceptre in his hand, and a sword borne before him, rode through the principal street to the church, dutifully attended by all the rest on horseback. The clergyman in his best robes received him at the churchyard stile and conducted him to hear divine service. On leaving the church he repaired, with the same pomp, to a house provided for his reception. Here a feast awaited him and his suite, and being set at the head of the table he was served on bended knees, with all the rites due to the estate of a prince. The ceremony ended with the dinner, and every man returned home.

Should probably be better understood in terms of medieval "Feast of Fools" and similar festivals. For more on which, see Sacred Folly: A New History of the Feast of Fools.

The idea of a "sacred king" that was sacrificed when disaster happened, or to promote the harvest, basically developed from there; especially in an early British/Anglo-Saxon context, and sometimes conflated with the supposed human sacrifices conducted by druids as recorded by Julius Caesar during the Gallic Wars, a la the film The Wicker Man (1973).