kitchen area; family circumstances
A somewhat dated or literary term referring to the kitchen and its immediate surroundings, or by extension, the domestic or financial situation of a household. The second gloss 'family circumstances' is a figurative extension of the kitchen-as-heart-of-the-home idea.
A house with a spacious kitchen area is easy to cook in.
That family seems to be in difficult financial circumstances.
Compound of 勝手 (katte, 'kitchen' in older usage) + 元 (moto, 'origin' or 'vicinity'). The exact historical derivation is uncertain, but the word likely referred to the area around the kitchen and later extended to the household's domestic situation.