The heart was an organ found in many biological organisms that was responsible for pumping blood through the circulatory system.
In humans, the heart is usually found on the left side of the thorax, underneath a bone called the breastbone. The human heart has four chambers, a left and right atrium, and left at right ventricle. Connected to the lungs, the heart helps re-oxygenate blood before supplying it to the rest of the body.
The Vulcan heart is positioned differently than that of the human heart, located on the right side of the body underneath the lung. (Star Fleet Medical Reference Manual) Doctor Leonard McCoy, treating Commander Spock after he had been shot, remarked that Spock would have died if his heart had not been where the liver was in a human. (TOS episode: "A Private Little War") Captain Ronald Tracey later used the fact that the Vulcan heart was in a different location in an attempt to prove to the people of Omega IV that Spock was the devil, and that because of this Spock had no heart. (TOS episode: "The Omega Glory")
In Malcorians, the heart is located in the area of the body where the digestive organs would be in a human body, and the digestive organs are where a human's heart would normally be. Malcorian doctors treating a disguised Commander William Riker were unable to find a heartbeat where they expected, and were surprised to find a heartbeat in his upper chest. (TNG episode: "First Contact")
The heart is one of the most vital organs in a humanoid body. A serious injury to the heart can be life threatening, and humanoids cannot live without a functional heart. By the 24th century artificial hearts were used routinely to replace hearts that cease functioning due to disease or were otherwise damaged. Captain Jean-Luc Picard's heart was replaced after he was stabbed directly though the heart by a Nausicaan during a brawl. (TNG episodes: "Samaritan Snare", "Tapestry") Later, when the heart of Captain Kira Nerys was damaged by Taran'atar, Doctor Julian Bashir was unable to repair the heart, and was forced to replace it with an artificial heart. (DS9 novel: Warpath)