It is the predecessor to the Pink Sock phenomena. When you are being anally annihilated, and your partner pulls out their dick or fingers, or whatever form of anal probe you decide to use, so fast that your intestines actually dingle from your ass. Not to be confused with dingleberries.
The only way to cure a brown sock, is for it to transform into a pink sock. One must turn around and tell their partner to clean their brown sock with their mouth until they are cured and have a nice pretty pink sock.
1: So I was getting ass fucked by Joey the other day and when he finished he pulled out so fast I got a brown sock.
2: Did he fix it for you?
1: Well I turned around furiously and said suck on my brown sock bitch. And he did. So now I have a pink sock like you.