After the child kept begging, his mother finally relented and let him watch TV for another half hour.

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"（态度）软化、让步"的意思。