Since Mr. Woodifield had his stroke, his wife and daughters have been taking care of him. To this end, they keep him boxed up in the house for every day of the week except Tuesday. That's the day when he's allowed out for the day, dressed and brushed before heading off to the City.

The City is short for "The City of London," which is Great Britain's financial center, the equivalent of Wall Street. We can infer from this that Mr. Woodifield, who's recently retired, used to work here, and takes the opportunity of his weekly outing to catch up on old friends and work colleagues, like the Boss in the story.

Though what Mr. Woodifield actually gets up to every Tuesday is an absolute mystery to his wife and daughters. They don't know for sure what he does, but they presume that he makes a nuisance of himself to his friends. Although that's not quite an accurate description of Mr. Woodifield's meeting with the Boss, he does inadvertently make a negative impact on his old friend by broaching the painful subject of his son's death. It is this that provides the catalyst for the Boss' cruel treatment of a fly after Mr. Woodifield has left.