It’s a term from my favourite show Firefly. It’s basically a group of people who stood up for what they believed in and were on the losing side of a big war in the show.
After the show got cancelled the fans called themselves Browncoats and banded together to help try and get a film made - a few years later with the help of the fans and the cast and crew of the show the film was made, called Serenity.
Now a lot of fans call themselves Browncoats :)
Sorry long answer haha, I love Firefly!