It means to begin a friendship, or a conversation. This phrasal verb can't be separated.

eg:We struck up a friendship on the first day we met.
While he was waiting in the queue, he struck up a conversation
with the person in front of him.

strike up的意思为发起，但多数时候用于发起谈话。strike和up不能分开。

例：我们第一次见面就成为了朋友。

排队的时候，他开始和前面的人聊天