The singer's father, the keeper of the Eddystone Light, had three children by a mermaid. Now he is gone (deserted? eaten by cannibals?). The boy meets his mother, who asks of her children; they live the troubled lives of half-humans
Perhaps the most-parodied song of all time. I know of "The Keeper of the London Zoo," "The Keeper of the Asteroid Light," and "The Man at the Nore" -- which is sort of a self-referencing parody.
Richard Dyer-Bennet has been credited with creating the final verse of the common version ("The phosphorus flashed in her seaweed hair..." -- bad science, incidentally, since there is almost no free phosphorus in the ocean; it's a necessary chemical for life, but not very common; every atom finds a home in some creature's DNA. Many ocean creatures are, of course, phosphorescent -- but not due to phosphorus).
The Eddystone Light is famous for representing a revolutionary design. It was the first lighthouse designed as a smooth cylinder -- important because it would help the lighthouse survive heavy seas and storms. Most later lighthouses, of course, have followed this design. - RBW