According to Fernando J. Corbató who worked on Project MAC in 1963, his team was the first to use the term daemon, inspired by Maxwell's demon, an imaginary agent in physics and thermodynamics that helped to sort molecules:
We fancifully began to use the word daemon to describe background processes which worked tirelessly to perform system chores.
In the general sense, daemon is an older form of the word demon, from the Greek δαίμων. In the Unix System Administration Handbook, page 403, Evi Nemeth states the following about daemons:
Many people equate the word "daemon" with the word "demon", implying some kind of satanic connection between UNIX and the underworld. This is an egregious misunderstanding. "Daemon" is actually a much older form of "demon"; daemons have no particular bias towards good or evil, but rather serve to help define a person's character or personality. The ancient Greeks' concept of a "personal daemon" was similar to the modern concept of a "guardian angel"—eudaemonia is the state of being helped or protected by a kindly spirit. As a rule, UNIX systems seem to be infested with both daemons and demons.
A further characterization of the mythological symbolism is that a daemon is something which is not visible yet is always present and working its will. In the Theages, attributed to Plato, Socrates describes his own personal daemon to be something like the modern concept of a moral conscience:
The favour of the gods has given me a marvelous gift, which has never left me since my childhood. It is a voice which, when it makes itself heard, deters me from what I am about to do and never urges me on.