He was based in Birmingham during the war.

was 是 be 动词的过去式，表示过去的状态。 based 是动词 base 的过去分词形式，base 本意是"基地、基础"，在这里表示"驻扎、以...为基地"。 in 是介词，表示"在...地方"。 was based in 是一个固定搭配，表示"驻扎在..."或"以...为基地"。