Demon

"Demon" is the Covenant name for all Spartans, but is most commonly used in reference to the Master Chief.

It is theorised 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.

Gameplay
In gameplay, when Covenant warriors encounters 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 (Gravemind (Level)|Uprising (Level)). The Prophet of Truth is the only member of the Covenant that has referred to John-117 as the Master Chief ("This demon... this Master Chief").

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!", "The Prophets shall reward me well for that!", or more rarely, "Ha! And I'm not even The Arbiter!"