"We have done the impossible, and that makes us mighty". It's a quote from Joss Whedon's world found in the TV Show Firefly & movie Serenity. Browncoats are fans of that world, who liked it too much to let it just die after half a season on TV. Fans support for the show led to the story being continued thorough the movie & other genres.
Some fans know all the episodes by name & can quote lines from them, some fans dress up as characters in the show at conventions, while others just like to watch the show. No matter what, Browncoats believe that because of this show, the world is a better place.
For more info on the show, please check out the following links, or better yet, set yourself down in front of your TV & watch it for yourself. You'll be glad you did & we will see you in the 'verse.