Literary or formal term for a person one has known for a long time. In everyday speech, 昔の知り合い or 古い友人 are more common.
He is an old acquaintance of my father's, apparently going back to before the war.
故旧を訪ねて故郷へ戻った。
I returned to my hometown to visit an old friend.
relatives and old friends
Compound of 故 (old, former) and 旧 (old, ancient). The exact historical derivation is uncertain, but the combination conveys the idea of a long-standing relationship.