The quote describes a character who coughs in a distinct manner, likened to a sheep clearing its throat, suggesting a certain refinement or social propriety. This imagery evokes an old-world charm and hints at the character's attempt to fit into a particular social context, highlighting their somewhat awkward demeanor.
Wodehouse's writing often employs such whimsical descriptions that add depth to his characters. This particular cough serves to portray the character's nervousness or deference, establishing both their personality and social standing in a humorous way typical of the author's comedic style.