After their children's persistent pleas, the parents relented and allowed them to go camping.

relented 是动词 relent 的过去式，relent 由前缀 re-（表示"再次"）和拉丁词根 lent（"弯曲"）组成，原意是"再次弯曲"，引申为"态度软化、变得温和"。在这里表示父母从原先的强硬态度转变为同意。