In this instance, the point of showing you the king's funeral was primarily that it provided Lord John with his moment of enlightenment regarding Jamie's motive for remaining at Helwater. Secondarily, it shows a historical turning point that a) anchors the reader in time, b) metaphorically underlines the conclusion of the Grey brothers' quest, c) marks a turning point in Lord John's relationship with Jamie Fraser, and d) opens the door to a new phase of both personal and public history--for George III (who was the grandson, not the son, of George II) is, of course, the king from whom the American colonies revolted, and we see in the later books of the Outlander series just how that affects the lives of Lord John, Jamie Fraser, and William.