Aka the Independents, the Browncoats (known as such because they wore brown leather trenchcoats) fought against the Alliance six years before the time the show starts. Unfortunately, they lost. Defeated at the Battle of Serenity Valley, the brown-coated rebels lost their cause and had to bow down to the might of the Alliance. Some, however, didn’t take too kindly to being ground under the heel of what is a seemingly corrupt government, and would seek every opportunity to undermine that authority.
Browncoats is also the collective term for the Firefly fandom.