In Judaism the concept of dying is as much a part of the cycle of life as living is. Judaism teaches that a person is brought into this world in order to live a fulfilled life that draws the person closer to God, and also leaves a positive imprint in the world after they are no longer here. That is the idea of adding the words "for a blessing" or "may his/her memory be blessed" — in effect we are stating that the deceased was a good person and that he or she should be regarded as such in the earthly and in the spiritual realms.
There is a verse in the Book of Proverbs that is actually a source of our custom to say or write this phrase after saying the name of someone who is deceased. The verse states, "The mention (or memory) of a righteous person is for a blessing.” (Prov. 10:7) The words in Hebrew for this are “zecher tzadik l’vracha”, which when made into an acronym is “z’tl” or “zatzal”. Some people say this only after the name of a clearly righteous person, since that is the literal sense of the verse, but many people say it after virtually anyone’s name since we are not in a position to judge who is truly a “righteous person”.
