。
The heating in the dorm is broken.
Literal
Dormitory [possessive-の] heating [subject-が] is-malfunctioning [explanatory-んです].
故障している (is broken/malfunctioning) uses ~ている for a resulting state. The contraction してる is casual. んです (explanatory) signals the speaker is providing background — likely explaining to maintenance why they need help. This combination of contracted verb + polite んです is very natural in spoken Japanese.