From Halopedia, the Halo wiki
A daemon is a computer program that performs its function "in the background" during the normal operation of a computer system, for example providing security services, performing maintenance operations, communication with peripherals or other subsystems, or more.
During the Battle of Installation 00, the daemons in the Ark's computer systems were alerted to the presence of the formerly imprisoned AI Mendicant Bias, which had reconstituted itself using the lost fragment aboard the Covenant's Forerunner Dreadnought. The daemons attempted to confine Mendicant and prevent it from communicating with John-117 via the terminals, although they were not wholly successful.
In Greek Mythology and cultural belief, daimons are lesser divinities or spirits similar to ghosts, chthonic heroes, spirit guides, forces of nature, or aspects of the deities themselves. Much like the computer programs that would be named for them, they were often "behaviors" of divine or spiritual activity, operating on a subconscious level.