The liver is an organ that is vital to metabolism. It filters toxins out of the blood and produces bile, which plays an important role in the digestive system.
The Vulcan heart is located where a Human's liver would be. (TOS: "A Private Little War")
Among the many organs found in a secret laboratory on a Vidiian planetoid was the liver of a Kazon. (VOY: "Phage")
Liver is a delicacy among many species. Phlox was fond of chicken liver with grated cheese, (ENT: "Storm Front") and slug liver is enjoyed by Ferengi. (DS9: "The Assignment")