Explain the actual/hidden meaning of the sentence particularly the italics part.
In the vestibule below was a letter box in which no letter would go,and an electric button from which no mortal finger could coax a ring . Also appertaining thereunto was a card bearing the name "Mr. James Dillingham Young".
The "Dillingham" had been flung to the breeze during a former period of prosperity when its possessor was being paid $30 per week.
O. Henry is describing a building in a poor part of town where the rents are low. No letter would go into the letter box (or mailbox) either because Jim and Della never received any letters or because the letter box was so old and dilapidated that the little door could not be opened. Perhaps the key to the box had been lost long ago and the owner had never bothered to replace it. The same applies to the electric button, which was probably right below the letter box. In a building like that the little amenities such as electric buttons get out of order and are never fixed. There is no manager or maintenance man on the premises. If anybody comes to visit the Youngs, the visitor will have to find their apartment and knock on the door. Little details like this show O. Henry's sensitive observation of details and his skill at making deductions from them. Another example of his talent in this regard is his description of "a pier glass in an $8 flat."
Perhaps you have seen a pier glass in an $8 flat. A very thin and very agile person may, by observing his reflection in a rapid sequence of longitudinal strips, obtain a fairly accurate conception of his looks.
The fancy calling card bearing the engraved name Mr. James Dillingham Young is intended to show that the Youngs have come down in the world. Jim had been earning $30 a week but was earning substantially less now, possibly because of a recession or depression. The $8 rent would mean $8 per week.
O. Henry had had a hard life and had undoubtedly lived in such flats himself. He was living in a cheap hotel in Manhattan at the time of his death in 1910. His writing is characterized by compassion for the underprivileged, who were the people he knew best.