Boyfriend/girlfriend drop refers to the act of subtly adding the fact that you have a boyfriend/girlfriend into the conversation in order to deter anyone who is potentially interested in you. 

“扔男友/女友”指在聊天的时候不经意提起自己有男朋友或女朋友的事情，目的是为了击退某个对你感兴趣的人。

For example:

She thought I was interested in her and boyfriend dropped me in our last meeting.

她以为我对她有兴趣，于是在上次见面的时候就告诉我她有男朋友了。

这个说法大概是来自于英语中另外一个使用较广的表达name drop，名词形式为name dropping，也就是我们平时说的“拽人名”。