When Ms. Sommers feels the stockings, they glide "serpentlike" through her fingers. What does a serpent often symbolize in Western culture?
As a result of their association with the Devil in the Garden of Eden, serpents, in Western culture, are often symbolic of temptation. The Devil tempted Eve to sin when he offered her an apple from the tree from which God said she and Adam must not eat. Mrs. Sommers, a woman who has had to make due with little for herself so that she could adequately provide for her children, is terribly tempted in this story by those silk stockings.
At first, she decides to use the money judiciously: paying a bit more for one child's shoes so that they will last longer, new clothing for her children rather than patching up the old and worn, some stockings for her girls, and even a hat for each of them. Having entered the store, however, and absentmindedly placing her hand upon something soft and pleasant, Mrs. Sommers becomes tempted to purchase something lovely for herself for the first time in a long time. The girl at the counter speaks to her, and "she [goes] on feeling the soft, sheeny luxurious things—with both hands now, holding them up to see them glisten, and to feel them glide serpent-like through her fingers." Tempted by the thought of treating herself, Mrs. Sommers purchases them and immediately exchanges her cotton stockings for the new silk ones. The temptation was too great for her to pass up.
Snakes in Western culture are a symbol of sinfulness, deceit, and just general evil.
The reason for this probably goes back at least to the story of Adam and Eve. In that, the serpent lures Eve into sin with his deceit. So the Judeo-Christian tradition starts with a snake causing the first sin to happen.
The snake is also connected with sexual sin in particular. This is partly because the sin of Adam and Eve is often seen as being connected with sex. It's probably also connected to the shape of the snake and the sensuality of the way it moves.
At any rate, snakes are definitely connected with deceit and sin in our culture.