This term originated in theatre, coined by the venerable theatre critic Allison Ward. It can refer to a variety of situations involving a bro, but the following are the most common uses of it:
1)A friend who is not really your friend, thus for show
2) a bro in your show, thus a "show bro"
3) a bro who aids your show, whether by working in the crew, or driving you around to obscure prop shops to pick up swords.
4) a bro of whom you are proud, and thus flaunt continually
1) "I though that Karen was my friend, but she just told my secret to everyone!"
"Yup, she's a show bro for sure."