The line you have quoted comes just after Della has had to accept the fact that she has been unable to save enough money to buy her husband, Jim, a present worthy of the love that she has for him. The introductory paragraphs of this classic story stress the harshness of the circumstances that Jim and Della face in their lives and how poverty affects them. After Della finishes having a good cry because she is upset about the fact that it is Christmas tomorrow and she won't be able to buy a present for Jim, she looks out of the window, and sees her mood reflected in what she sees. Note the repetition of the word "grey" in the quote you have identified. This of course summarises Della's grey life at this point, as she has to cope with her expectations of surprising Jim with a lovely present being crushed. Note how the two are so closely intertwined in the narrative:
She stood by the window and looked out dully at a grey cat walking a grey fence in a grey back yard. Tomorrow would be Christmas Day and she only had $1.87 with which to buy Jim a present... Many a happy hour she had spent planning for something nice for him. Something fine and rare and sterling--something just a little bit near to being worthy of the honour of being owned by Jim.
Thus the quote you identify is explicitly linked to the sense of disappointment and lack of hope expressed by Della. She has just been forced to accept that her plan of buying a worthy present for her husband has come to naught, and her world is tinged with bleak despair as a result.
This line comes just after Della has finished crying because she has only $1.87 to buy a Christmas present for Jim. She is trying to regain her composure and develop some kind of plan that would enable her to obtain more money so she can buy a nicer, more appropriate present for him. However, nothing has come to mind as an idea for how to make this happen quite yet. Her attitude and emotion as she looks out the window matches the surroundings in which she is living - everything is the same colorless, hopeless, dull shade of gray. There is no variety, no glint of color, no hope of anything to break up the monotony, no prospect (at this moment) of improving her financial situation.