What's the difference between an appendix and a cecum, and what are their functions?
In herbivores the Cecum is an area that stores plant matter and helps digest it via symbiotic bacteria. Carnivores have smaller Cecums because meat is easier to digest than plant matter. In humans the Cecum is also an anatomical landmark that delineates the change from small intestine (a digesting organ) to the large intestine (mostly a capacity/storage organ).
The Appendix is a small, previously thought "superfluous" fleshy worm-shaped organ at the junction between the small and large intestines. Recent research posits that the appendix is sort of a harbor for a person's gut flora that can re-populate the intestines should the existing bacteria die or get removed (diarrhea being the most common cause). It can also become infected, inflamed, and require surgery to remove (Appendicitis).