In the first sentence of "The Fly," Mr. Woodifield comments that the boss is very snug in his office. He goes on to repeat the word, saying, in a wistful and admiring voice, that the office is snug.
The primary meaning of snug is "comfortable" or perhaps "cozy." It is somewhat ironic that Woodifield employs this description of a business office, since it is a word more often associated with home than work. Woodifield used to work in an office in the City of London, as the boss now does, but he was compelled to retire after having a stroke. He now spends most of his time at home, with his wife and daughters.
Woodifield makes it clear that he feels more at home in the type of office where he used to spend his days than he does inside his own house. The boss offers him whisky, which he is not allowed at home, and he is also able to smoke cigars. These comforts, along with the "great, green-leather armchair" give the boss's office the atmosphere of a gentleman's club. Quite apart from the physical coziness of the office, Woodifield has evidently spent his life in such masculine environments, and being stuck at home, surrounded by women, is alien and uncomfortable for him.