、。
When dinner was over, we moved to the living room.
Literal
Dinner [subject-が] finish-[then-で], we [topic-は] living-room [to-へ] move-[past-った].
済んで is the te-form of 済む ('to be finished'), acting as a temporal sequencer: 'finishing, [we]...' — i.e., 'once it was done, we...' 居間 ('living room') is the Japanese home's everyday family space, contrasted with 応接室 ('formal reception room'). 移る ('to move, shift, transfer') is intransitive; the people do the moving.