Della has just finished crying about the fact that she only has one dollar and eighty seven cents to purchase a Christmas gift for her beloved husband, Jim.  She "flop[ped] down on the shabby little couch," having had only so much luck after "bulldozing the grocer and the vegetable man and the butcher" to save money, a penny at a time, for months.  Once she has cried herself out, Della powders her cheeks, goes to the window, and looks out "dully at a gray cat walking a gray fence in a gray backyard."  This is a very dismal and dreary description, and it gives us further insight into Della's feelings.  Her husband's salary was cut by a full third (an insanely high amount for a pay cut), from thirty dollars to twenty dollars per week, and "Twenty dollars a week doesn't go far.  Expenses had been greater than she had calculated.  They always are."  Della is disheartened, dispirited, and maybe even a little bit depressed. The morose description of her gray surroundings mirrors her emotional state.

The grey cat reflects the surroundings, the neighborhood in which Jim and Della live - "a grey cat walking a grey fence in a grey backyard." O. Henry is painting a word picture of the environment, which is colorless and drab, and of their situation in life. Jim and Della don't have much in the way of color or excitement in their lives due to the financial state of their household. They live in a small and very inexpensive apartment, probably in a less-than-desirable location. Grey is the color that best describes much of their existence - not the black of complete hopelessness and despair, but no concrete reason to see anything better anytime soon.