Vulcan finger-touching was a ritualistic form of affection among Vulcans. The behavior was also occassionally used between a Vulcan and a member of another species, such as between Sarek of Vulcan and Amanda Grayson of Earth. (TOS: "Journey to Babel") Another example of this was between Spock and a Romulan female commander. (TOS: "The Enterprise Incident") Finger-touching was also sometimes involved in sex between Vulcans. (Star Trek III: The Search for Spock) Some Vulcan marriages also incorporated finger-touching. (ENT: "Home")
It can also be noted that in the later star trek movie, Star Trek: Into Darkness that Kirk and Spock touch fingers while Kirk is dying. Finger touching may also be seen in relationships such as this one, with friendship or endearment.