I think of demons as the embodiment, or a particular aspect, of evil. There’s no reasoning with it, no appealing to its “humanity” – despite appearances and actions they are not human and we can not truly understand or identify with them, there can be no dissuading or sating its desires. It can take human form (among others), perhaps it can be driven off but it doesn’t die, it feeds off us, it ferments its evil in us – whispering over and over – twisting us until our desires can only be fulfilled by become it. Above all, a powerful demon is unique – as much as any character, it has its own persona. Nothing positive should come from the end of a demons machinations, a victory is pyrrhic at best and bleakly temporary, leaving desolation, death, pain, and suffering in its wake.
Check out Hellriaser, Devil’s Advocate, Demons, Prince of Darkness, Pumpkin Head, Rosemary’s Baby, Insidious they don’t all use “demons” exactly but use interesting ways of portraying what could easily be a demon. Even The Thing particularly when trying to determine who’s human and who isn’t, that sense of tension, distrust, and dread.
In general, horror is about suggestion and atmosphere; nothing is more terrifying than what the viewer conjures in their own imagination. Make it believable, at least enough to make the audience suspend their disbelief, think “what if”, and see themselves as vulnerable. It could be anyone, anywhere just plant the seed, provide the setting, and allow them scare themselves silly. One of the things a demon allows for is straddling the border of human and monster. Some find it all the more horrifying to discover it was a person that was the root of the evil others an inhuman monster – a demon can be portrayed either way. Hinting at its otherworldliness, providing just the suggestion that it may not be human always making the viewer wonder. Or by exposing it’s unrelenting monstrousness in paralyzing, heart stopping, fear as it consumes its prey.
Sorry for making that sort of a “nebulous” answer but I think all that goes to what makes a demon terrifying – it’s not always the same thing – it really depends on how its being used and portrayed.