Learn Hardcore Norwegian: En postkasse står bak huset. - A mailbox stands behind the house.

Norwegian has two grammatical genders in the written standard (Bokmål): common (n-words) and neuter (t-words). The indefinite article en is used with common-gender nouns, while et is used with neuter nouns.

postkasse is a common-gender noun ⇒ en postkasse
hus is neuter ⇒ et hus

Why is huset in the definite form, while postkasse remains indefinite?

Definiteness in Norwegian is marked on the noun itself with a suffix:

Neuter nouns like hus add -et for the definite singular: hus → huset (“the house”).
Common-gender nouns add -en for the definite singular: stol → stolen (“the chair”).

In this sentence, postkasse is being introduced for the first time (so it’s indefinite – en postkasse), whereas huset is assumed known or contextually given, so it appears in the definite form (huset).

What exactly does bak govern here? Do I need another article or case ending?

bak is a preposition meaning “behind.” In Norwegian you place it directly before the noun (in its correct form):

indefinite: bak et hus (“behind a house”)
definite: bak huset (“behind the house”)

There is no extra article or case ending beyond the normal definite suffix -et on huset.