Copremesis is the vomiting of fecal material.
This is caused by intestinal contents backing up above an intestinal obstruction. The obstruction could be due to strictures (narrowing of the intestinal lumen), volvulus (twisting of the intestine to close off the lumen), or mechanical blockage through an accretion of stool or a tumor.
Stool backs up from the point of obstruction until it fills the stomach and is vomited up. This is associated with severe abdominal pain and distention, and a feculent breath odor (breath literally smells like shit). It can lead to jaundice (bilirubin not being eliminated from the body through the stool is reabsorbed in the intestine), and is generally a medical emergency.
I have fortunately only observed this once, but it is a memory that will stay with me forever.. especially the smell :-*