Explain to me the grammatical usage "Had had"?

"I started out on the five-mile swim after I 'had had' a good rest", is used when one is writing about an event that occurred before the time of writing, and could be substituted with "I started out on a five mile swim after having had a good rest overnight". "I started out on the five-mile swim after I 'had' a good rest", should not be used at all. However, you could write, "I had a good rest overnight and then started out on a five-mile swim". So it comes down to indirect and direct speech.