What need is awakened in Mrs. Sommers by the pair of silk stockings, and what inner conflict does this reveal in "A Pair of Silk Stockings"?

Her desire to purchase the silk stockings for herself indicates a need in Mrs. Sommers for self-indulgence.

When Mrs. Sommers becomes "the unexpected possessor of fifteen dollars," she considers for days what she will buy with the windfall she has received. In her mind she considers what is needed for the children: 

The vision of her little brood looking fresh and dainty and new for once in their lives excited her and made her restless and wakeful with anticipation.

Clearly, Mrs. Sommers has unselfish intentions, and she possesses the dutiful thinking of a mother as she prepares to take the trolley one day and make her planned purchases. However, on this day she is "a little faint and tired"; in fact, she has forgotten to eat before leaving home. So, after she enters a shop, she sits down at a counter; while resting there, her hand inadvertently brushes against something "very soothing, very pleasant to touch." She notices that her hand rests upon a pile of silk stockings that have a placard near them which advertises a price reduction. Noticing her, a young clerk asks Mrs. Sommers if she would like to look at the silk hosiery. Blushing, Mrs. Sommers inquires, "Do you think there are any eight-and-a-half among these?" and the clerk shows her several in different colors. Mrs. Sommers selects a black pair and holds them up, pretending to examine their texture. Quickly, the clerk assures her that their quality is excellent.

"A dollar and ninety-eight cents," she mused aloud. "Well, I'll take this pair." She handed the girl a five-dollar bill and waited for her change and her parcel.

Once she has made this purchase, Mrs. Sommers is eager to discard her cotton stockings and wear her new silk ones. In the ladies' waiting room, she removes her old stockings and puts on her new ones. "How good was the touch of the raw silk to her flesh!" She revels in her indulgence momentarily. Then, she places her cotton stockings in her bag, puts on her shoes, and crosses over to the shoe department. Mrs. Sommers now fulfills her own desires as she purchases a pair of polished, pointed-tipped boots and kid gloves. 

Her change of heart is, perhaps, due to her exhaustion from years of being frugal and making personal sacrifices. Now, shopping for herself and indulging herself at a restaurant and a theater are Mrs. Sommers' escapes from her humdrum existence and her personal deprivation. In the theater,

... there was no one present who bore quite the attitude which Mrs. Sommers did to her surroundings. She gathered in the whole--stage and players and people in one wide impression, and absorbed it and enjoyed it.

Made powerless for years by her economic situation, Mrs. Sommers acts this day in feminine rebellion and delights in the small indulgences of the past.