I see it's an old topic, but I answer it anyway. Core is the people live there. Owner is the original owner Poland. Now, the territory is controlled by Poland. The province is inhabited by polish and german people. It's a border region right?
I first come across this core in Victoria 2. In that, it was casus belli if somebody had a province that have a core of your nation. (Hungary had a little CB for all neighbors because the 1920 Treaty of Trianon) Hungarians lived there, so Hungary had a core in that romanian, slovak etc. region. I don't know if it means any production bonus though, or if it's a CB in HoI3.
All times are (GMT -08:00) Pacific Time (US & Canada). Current time is 9:04:38 AM