The pressure in the esophagus (the tube connecting the mouth and stomach) can become abnormally very high. Because of this high pressure an analogy was drawn between the esophageal pressure and the pressure generated by a nutcracker giving the term – nutcracker esophagus:
R Fass, R Dickman. Nutcracker Esophagus-A Nut Hard to Swallow. Journal of Clinical Gastroenterology, 2006 40:(6) 464-466.
Besides nutcracker esophagus, there’s another medical entity known as nutcracker syndrome.
BONUS: The use of other less crushing kitchen utensils as analogies in medicine can be found here.