Food enters the stomach where acids break down the material. In the small intestine, the material has much more fluid and the body begins to move that fluid to the kidneys as further break-down occurs. By the time it reaches the large intestine, it becomes much more "formed". It passes through the colon, further through to the rectum where humans sense the pressure of a needed bowel movement. The BM then passes from the rectum and out the anus.
Note that in diarrhea, changes occur in how much fluid can be drawn off and excreted via the urinary system. In profound diarrhea, the matter is mostly fluid mixed with some formed excrement.
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By defecating. That is the process of expelling "solid" wastes out the large intestine and through the rectum and anus.
The end of the large intestine is the rectum, which empties into a colon, which leads to the anus.
Contractions that move in slow waves help to move solid material from the intestines.