Horror, like all genres, involves a moment of revelation, epiphany, or climax. However, unlike most genres, the epiphany in horror leads to a contradiction. Because while climax is usually followed by resolution, or denoument and catharsis, a true horror story can not really present catharsis. It presents revelation, and then...
In a horror story, the moment of revelation is the revelation of evil. It could be argued that in some horror, it is just something grotesque or gory, but allow me my more conceptual difference. People realize evil, which is often the same as realizing their own guilt or failure. There are some "high culture" examples of this, from Thyestes unknowingly eating his own children in Greek myth, the narrator's guilty breakdown in The Tell-Tale Heart, or the endless torment of the nazi officer in Deaths-Head Revisited. There are also examples in more popular culture: Mrs. Deagle's fate in Gremlins or the popular cliche of sexually promiscuous teens being murdered in slasher films. (Obviously this "revelation of guilt" can be used in some pretty socially problematic ways, as when it is used to shame sexuality, but the point remains). In any case, most horror has to have a moment where evil is revealed, where an internal moral secret is turned into an external, physically dangerous one. This is the moment of epiphany that horror revolves around, what can allow the audience catharsis.
The problem is, that by its nature, horror can not grant catharsis. As a counter example, let us use an example of a story that has horror elements, but ruins it with catharsis: A Christmas Carol. After confronting ghosts, external spirits that show him his internal flaws, what does Ebenezer Scrooge do? He reforms. He realizes the error of his way, realizes there is another direction, and finds the light. Our moment of catharsis, of realizing and confronting evil, leaves him to choose good. And for that reason, this story is not horror.
In a real horror story, I would say, there is no choice. Especially when it deals with real world evils. In Deaths-Head Revisited, the nazi officer is beyond redemption, after he realizes his own evil, there is nothing he can do. He is doomed to face his own evil forever.
So this is the contradiction of horror. It offers us an epiphany, in this case, the epiphany of evil, and then ends there. From an artistic point of view, we are offered a climax with no resolution. A resolution would negate the epiphany. We are just left with the open moment of epiphany. And, in horror, when the creator is doing something right, this succeeds. The audience is left with something, even if it is hard to describe it under the traditional structure of plot development. Perhaps what the audience gains is just a sadistic moment of schadenfreude, perhaps these moments of horror are only used to blame or punish people, but I do believe there is more to be gained than that, although I can not say exactly what.