They introduced meetings at Miss Kenton's parlour which were held every evening and served the purpose of discussing house running.

served 是动词 serve 的过去式，serve 的意思是"服务、满足、适合"。 the 是定冠词，在这里特指前面提到的"会议"。 purpose 是名词，意思是"目的、用途"。 served the purpose 是一个固定搭配，意思是"达到目的、满足需求"，在这里指"这些会议实现了讨论家务管理的功能"。