The Kiss of Death is usually given to someone as a sign that they are about to die. They are not going to die from a poor state of health, but usually by the skilled hands of a hired assassin, or by the blundering ways of some unreliable henchman. The kiss is given because the soon-to-be-victim has usually done something offensive to the giver and must be taken care of in a "traditional" manner.
Among the clichéd traditional ways of disposal might be to "sleep with the fishes," or "whack da dude," and to stick someone's head in a vice and crank...come to think of it, that one might have been somewhat original. The Kiss of Death is often associated with the Italian Mafia.
One of the most famous kisses of death is in The Godfather Part II. Al Pacino, as Don Corleone, gives his brother Fredo Corleone, played by John Cazale, the kiss after he discovers Fredo betrayed him by helping in an assassination plot.
It is documented that the Kiss of Death probably stems from the betrayal of Jesus by Judas. The betrayal is in Matthew 26:48-50. Jesus kisses the one, Judas, who betrayed him.