When you go into someone's bathroom and it stinks like shit but you only see brown water into the toilet (brown sauce).
When you don't have time to flush a second time after crapping and have to leave a standing bathroom with brown water still into the bowl.
"Yo Ray! I know you done shit in here! Come and finish your flushing. I don't want none of your brown sauce shit splashing up on my ass. You nasty Ray!"
The leaky excretions that are a byproduct of diarrhea. Also is used to reference the Cleveland Browns and can be used as a battle cry whenever the Browns score.
"Last night my friend had a steak and cheese and then exploded brown sauce all over the bathroom."
Friend 1: "What's the score of the game?"
Friend 2: "24-7, Cleveland's killing New England."
Friend 1: "BROWN SAUCE!!!!!!"