Demon

"Demon" is the Covenant name for all Spartans , but is most commonly used in reference to SPARTAN-117.

It is theorized that Covenant beliefs show a Demon (the Spartans) helping the unholy enemy (humanity) to destroy the great sanctuaries (The Halos), but this is speculation. There is no actual information on why the Covenant refer to Spartans as Demons.

The Covenant fear the Spartans because of their ability to destroy hundreds of Covenant soldiers. They particularly fear the Master Chief because of his destruction of Alpha Halo.

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.

Gameplay
In gameplay, when Covenant warriors encounter the Demon (Master Chief), they usually engage him with extreme caution. Grunts and Jackals have a tendency to retreat upon the Demon killing their Elite 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 as the 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 soldier. This can be noted in gameplay during 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 has died by my hand"; "I have earned my Journey!"; or more rarely, "Ha! And I'm not even The Arbiter!"

When the Demon throws a grenade, an Elite (and sometimes Grunt in Halo 2 will usually say "Demon Flare! Scatter!", regardless of the grenade type. When an Elite throws a grenade, he yells "Holy light!" or "Cleansing flame!"

Halo 3
While fighting with Elites on your side, they will call you demon, perhaps out of respect or to signify your rank as a Spartan. Later in the game, the Elites begin 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 refers to you as "Spartan" after destroying a Scarab on The Ark.