In the Northern and Southern Dynasties (南北朝,420-589AD) when the State of Chen (陈国) was facing its demise, Xu Deyan (徐德言), husband of the princess, broke a bronze mirror into halves.
南朝的陈国将要灭亡的时候,驸马徐德言把一面铜镜破开。
Each of them kept a half as tokens in case they were separated.
他跟妻子各留下一半。
Soon afterwards, they did lose touch with each other, but the two halves of the mirror enabled them to be reunited.
后来,夫妻二人真的失散了,凭借着各人留下的半面镜子,他们最终又得到团圆。
This idiom is used to refer to the reunion of a couple after they lose touch or break up.