It doesn't mean anything - at least not in English. The economy of the household would make sense, altho I didn't think to try it as an answer.
I'm not sure if there's a direct equivalent in English, but I think it refers to the school subject l Οικιακή Οικονομία, which is literally about economic (and other) household matters. I'm not sure if it is still a thing though. I haven't head about for a while. ._.
(That's just an assumption, since the sentence η οικονομία του σπιτιού, exactly as it is, doesn't make that much sense.:P)
Ah - well that would, I think, be home economics (which didn't exist when I was at school, but I think that's what they call it now).
Does οίκος have more of a sense of home about it than σπίτι?
Οίκος/οικία is a very formal term for home, mostly seen in written speech, in formal documents. Σπίτι is the term that's commonly used. ^.^
Ο οίκος is the word used for an important family, a dynasty or a company or a social welfare institution. Οικία is as Dimitra said, formal for "house".
And in some schools now called “ Home and Design Technology “ !
I took the expression to mean "household finances" which is how a family run their budget. This is the actual implementation of the school subject "home economics", and this expression is used in English today. How would I say "household finances" in Modern Greek? BTW if this expression isn't used that much today as the Greeks on this post seem to be saying it, why is it being taught to us?