The house that Sarah Penn was living in at the beginning of the story is old and rundown. It is stated early on in the story that Mrs. Penn had been living in that tiny house for forty years even though her husband, Adoniram, had promised shortly after they were...
married that he would build her a better one. If the house was difficult to live in when they'd just moved in, then clearly it must have become even more cramped and disheveled over time and as more people began to occupy it.
Mrs. Penn says that the bedrooms are too small, the cheap wallpaper is dirty and peeling, the pantry is tiny, and that some rooms, if not all, have no carpet. This dismal living space represents how patient and submissive Mrs. Penn has been for forty years. Her children grew up and she grew old in a house that even her own husband had declared not fit for them to live in. Her submission to her husband's stubborn refusal to build a better home or to even spend any decent amount of money on making the one they have cozy is literally reflected in the bleak state of their house.
However, it is also a symbol of how amazingly resilient, loyal, and hard-working she is. Mrs. Penn keeps her rundown home clean, tidy and in the best shape she is able, despite the horrible disrespect her husband shows her every day. She considers her job as a mother and a wife is to take good care of the house and all who live in it.
"She was a masterly keeper of her box of a house. Her one living-room never seemed to have in it any of the dust which the friction of life with inanimate matter produces."
Even her husband's mistreatment cannot keep her from performing her job impeccably. Later on in the story, she moves her things and her children into the new barn and this house also becomes symbolic of her character.
She describes the new barn as nicer than their old home, which subtly clarifies that her husband, although perhaps unknowingly, treated her and their children as worth less than animals. The barn was built for beasts of burden that serve Adoniram and that is, essentially, what the mother has been doing for forty years. She says that their new home will need partitions and furniture, symbolizing how open and honest she is finally being, but also how she'll need to create new boundaries in their lives and that she'll require better treatment.
Ultimately, their new home represents the better possibilities in their lives now that Sarah Penn finally got her husband to really listen to her.