There's a meeting going on in the next room.

Literal

Next [of-の] room [at-では] meeting-during [copula-です].

会議中 ('in the middle of a meeting') uses the ~中 (read ちゅう) suffix attached to 会議 ('meeting') to describe an ongoing state — productive across many nouns: 食事中 ('mid-meal'), 仕事中 ('at work'), 勉強中 ('studying'). では is the location topic-marker. Common office announcement.