Beekeeping
The queen is the only sexually mature female in the hive and all of the female worker bees and male drones are her offspring. The queen may live for up to three years or more and may be capable of laying half a million eggs or more in her lifetime. At the peak of the breeding season, late spring to summer, a good queen may be capable of laying 3,000 eggs in one day, more than her own body weight. This would be exceptional however; a prolific queen might peak at 2,000 eggs a day, but a more average queen might lay just 1,500 eggs per day. The queen is raised from a normal worker egg, but is fed a larger amount of royal jelly than a normal worker bee, resulting in a radically different growth and metamorphosis. The queen influences the colony by the production and dissemination of a variety of pheromones or "queen substances". One of these chemicals suppresses the development of ovaries in all the female worker bees in the hive and prevents them from laying eggs.
Honeymoon
Another practical source for the term comes from the early days in the life of a honey bee queen. Immediately after her birth within a hive, a queen bee leaves the hive over the course of several days, to meet up with multiple drones in separate drone congregation areas. She is inseminated with a lifetime of sperm, and then returns to the hive to remain there the rest of her life, laying eggs. The queen essentially goes away for a "honey-moon" and returns back, ready to live the rest of her life. The centuries old practice of beekeeping may have led to other folklore related to this "going away" before starting a life "in the hive" (back at home).