Slang for a Nazi or fascist pig. Derived from the brown shirts worn by the Sturm Abteiling (SA). Brown was the color of the Nazi party in the 20's and 30's, much as red and blue are respectively associated with the Republican and Democratic parties in the US now.
Side note - the Schutzstaffel (SS) primarily wore black uniforms.
Nazi: "I love Hitler. Mexicans suck."
Punk: "Fuckin' brownshirts. Let's bust some heads."
Mexican: "Hell yeah."
Soldiers in Hitler's storm trooper army, SA during the Nazi regime. They were called this because of the colored shirts they wore.
To call someone a brown shirt is to call them a Nazi soldier, usually hinting that they oppose human rights or freedom. This is a very serious insult, and in forums is used to Flame someone.
Hitler used many different forces to accomplish his goals when he rose to power. One of these forces were the SA, or Storm Troopers. The SA soldiers were called Brown Shirts.
"I don't like how that guy disagrees with my philosophy on <idea>. I'm going to call him a Brown Shirt so people associate him with Nazis, and his ideas are disregarded."