The Vulcan term for a person's living essence or soul, which can be passed to another mind before death and, in Vulcan belief, preserved after the body has gone.
The katra is the essence of a Vulcan: the memories, knowledge and personality that make up the self. A dying Vulcan can transfer it by mind meld to another person, who then carries it until it can be brought home to Vulcan.
The idea is introduced across Star Trek II: The Wrath of Khan and Star Trek III: The Search for Spock. Before entering the radiation chamber, Spock melds briefly with Leonard McCoy, who afterwards behaves erratically until Sarek realises what he is carrying. The katra is reunited with Spock's regenerated body on Mount Seleya.
Enterprise takes the concept further in The Forge, Awakening and Kir'Shara, where the katra of Surak, carried for a time by Syrran, passes to Jonathan Archer and guides him to the Kir'Shara. Katric arks were built to house such essences.