Heart

The Heart was an organ in many lifeforms. Humans had a single heart while Time Lords had a second heart. Some accounts indicated that a Time Lord would grow his or her second heart after the first regeneration (MA: The Man in the Velvet Mask) while other accounts indicated Time Lords had two hearts even in their first incarnation. (CC: Frostfire)

The Great Vampire, lesser vampires and Haemovores could only be killed by a stake through the heart. The more powerful Great Vampires needed their heart completely destroyed to be killed, commonly with a bolt of steel. The Time Lord's developed Bowships in order to destroy the hearts of great vampires. (DW: State of Decay, The Curse of Fenric)

Alternative definitions
Heart could also refer to the physical or ideological centre of a location. Looms were the heart of the Great Houses, (NA: Lungbarrow) or the Kandy Man's kitchen which was at the heart of Terra Alpha's governance system. (DW: The Happiness Patrol)

Heart can also refer to the change in emotional standing in an individual ie them having a "change of heart" such as Maldak saving the Governor and Peri Brown from execution on Varos (DW: Vengeance on Varos) or Alan Jackson changing his mind to move away from Sarah Jane Smith. (SJA: The Lost Boy)

Behind the scenes
The Man in the Velvet Mask attempted to retroactively explain why the Doctor appears to only have one heart in DW: The Edge of Destruction. However, the same ommission also appears in the Second Doctor story DW: The Wheel in Space. It is not concretely mentioned that the Doctor has a Binary vascular system until DW: Spearhead from Space.

Later stories would instead imply that injury or illness could temporarily stop one of the two hearts. (DW: The Mind of Evil, The Christmas Invasion, The Shakespeare Code)