As stated by the other writers, Bromberg is the German name for the former Prussian city that is now Bydgoszcz, Poland.
The Kingdom of Prussia had a system of provinces and municipalities like any other government.
In your case, "Bromberg Stadt, Posen, Prussia":
Bromberg Stadt = Bromberg City
(Provinz) Posen = Province of Posen
Prussia (i.e. Königreich Preußen) = Kingdom of Prussia
Note that Bromberg was its own kreis (Stadtkreis Bromberg) and also the center of a rural landkreis (Landkreis Bromberg) as well as a larger administrative region of the same name("Bromberg Regierungsbezirke).
The usual hierarchy of municipalities in Prussia was like this:
Königreich Preußen = Kingdom of Prussia;
Provinz = Province (e.g. Ostpreußen, Westpreußen, Posen);
Regierungsbezirke = Administrative region;
Kreis (Stadtkreis & Landkreis) = Districts (Urban Districts & Rural Districts [counties]).
These changed over time, so it can be a challenge to get an accurate picture of situation on any particular date.
These links may help:http://en.wikipedia.org/wiki/Bromberg_(region