Demon

"Demon" is the Covenant name for all Spartans , but is most commonly used in reference to John-117. This is primarily due to the fact that the Covenant fear the Spartans, because of their ability to destroy hundreds or thousands of Covenant soldiers. They particularly fear the Master Chief because of his destruction of Alpha Halo, and other Forerunner artifacts. Because they treat these as relics and the Forerunners as gods, it is possible they see the Master Chief as the opposite, a demon.

Demon could possibly mean a particularly powerful foe, and they might call Spartans "demons" because they rarely ever die, comparing to a demon's immortality and are bringers of great destruction and defeat (Master Chief and Installation 04). Also, a demon's immortality could be part of the UNSC myth of how Spartans never die, they only go MIA.

This may allude to the historical nickname Devil Dog, used for US Marines by the Germans during WWI.

Gameplay
In gameplay, when Covenant warriors encounter the Master Chief in combat and sight, they usually engage him with extreme caution. Grunts and Jackals have a tendency to retreat upon the Demon killing their Elite or Brute commander, or if they are the only soldier remaining. The Prophets and Brutes also refer to the Master Chief as the Demon. The Prophet of Truth is the only member of the Covenant that has referred to John-117 by his alternate name of Master Chief. It is theorized that Truth says this so the player knows who the demon is, as the term is not used in Halo: Combat Evolved.

If any Covenant soldier actually kills a Demon, it may be assumed they are given a very high reward for their success against this potent and dangerous adversary. This can be noted in gameplay during Halo 1: when John-117 dies, the nearby Grunts laugh crazily or shout "I did it! I'm the one!" and similar things. Also the nearby Sangheili laugh. In Halo 2 when the Master Chief dies, the nearby Elites say something along the lines of "The Demon is dead, I killed it! I killed the Demon!"; "The Prophets shall reward me well for that!"; "The Demon is dead! By my hand!"; "I have earned my Journey!"; or more rarely, "Ha! And I'm not even the Arbiter!".

When the player throws a grenade, an Elite (and sometimes Grunt) in Halo 2 will usually say "Demon Flare! Scatter!", regardless of the grenade type.

Halo 3
While fighting alongside your allied Elites, mostly Major Elites and Spec Ops Elites they will call you Demon, perhaps out of respect and deference or to signify your rank as a Spartan. Later in the game, the Elites begin clarifying and referring to you as Spartan, or sometimes, Human Champion; if you were to be killed anytime during gameplay, and the Elites witness this, one of them might say "The Human Champion is down!" The theory that "Demon" translates into "Spartan" is disproved in this game when Rtas 'Vadum and The Arbiter refers to you as "Spartan" after destroying a Scarab on The Ark. The Arbiter, Minor Elites and some Spec Ops Elites will sometimes refer to Master Chief as "Reclaimer", just like 343 Guilty Spark. This is most likely as a result of the new Human-Elite alliance, which makes the derogatory term Demon inappropriate. The Arbiter has probably taken the term from 343 Guilty Spark, who always refers to the Master Chief as Reclaimer. Like Rtas 'Vadum, however, he will usually simply refer to the Chief as Spartan. For example, when Johnson is killed by the Monitor, he says "I am sorry Spartan." If you die at the hands of Covenant soldiers like Brutes and Grunts, they will say things like "The Demon is dead!", "We are the Champions!" or on rare occasions, might say things like "I got the Demon's boots!", or "I call his helmet!". Often, one will shout (IWHBYD Skull off), "Who's dead now? Not me! Ha ha ha!"