Is there another word that translates well into English? I don't think I've ever heard anyone actually say "the province" in real life...
I say it all the time. Among other things it is an administrative division of Canada, like a state is in the U.S.
You happening to live in a location that is not divided into provinces does not invalidate the meaning or translation of "province"/"provincia".
Provincia is defined roughly as 'Administrative district of the territory of the state, consisting of a plurality of neighboring municipalities, the most important of which is its capital.'
In Britain is this a 'metropolitan borough'? As in, I'm in the Calderdale province in Yorkshire.
Ironically, an earlier version of the word lent its name to one of the first Roman conquests outside of Italy, in Gallia.