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1.
Similar to a night terror, a Brown Terror refers to a dream so mortifying that it causes a person to have a sudden and involuntary release of fecal matter whilst sleeping. Often accompanied by urination.

A Brown Terror often includes screaming as a result of realizing you just slept in your own shit.
Daniel saw his extremely unattractive music teacher play a box instrument in an erotic position with caused him to experience persistent Brown Terrors for the remainder of the week.
by KiddingKendrick January 02, 2011
 
2.
A bowel movement so violoent that it inflicts fear and/or pain.
"Sorry I am late, severe case of Brown Terror"
by Kev3345 June 12, 2009