The kitchen is very obviously Mary's domain, from the first time Rosicky mentions it. He says that he doesn't think Mary would like to have him "hanging round the kitchen too much," suggesting that it is her place of work.
The more extensive description of the kitchen cements this idea: the phrases used to descrbe it—"bright" and "warm," full of "handsome boys"—suggests that it is a vibrant place, the heart of the home. The long table is the first thing the narrative mentions about the kitchen, suggesting that it gave off an air of hospitality and of being able to accommodate many. The kitchen smells of "coffee and hot biscuit and sausage," all outward manifestations of Mary's affection for her family—and beyond. The story notes that while some people might have created a superficial impression of politeness in the kitchen if they had visitors, Mary did not do so—instead, there is no "best china" or good cutlery, no plain cloth to cover the bright oil cloth. Instead, Doctor Ed must "take us as you find us," according to Mary. The kitchen is as open to him as it is to anyone else who might venture into it, and because Doctor Ed is able to see it in all its usual vibrant brightness and warmth, he is equally able to feel Mary's own expansive kindness, as represented by her kitchen domain.