They were looking to expand their business internationally.

were 是 be 动词的过去式复数形式，表示过去的状态或行为。 looking 是动词 look 的现在分词形式，look 本意是"看"，在这里与 to 搭配表示"计划、打算"。 to 是不定式符号，与动词原形搭配表示目的或意图。 were looking to 是一个固定搭配，表示"曾经计划/打算做某事"。