Like many Gothic novels, the supernatural is largely besides the point here. This is really the story of a bad, bad monk. It's actually a fairly clumsy novel, when you think about it - Lewis couldn't seem to make up his mind as to how bad the monk should really be, so he veers between delighting in his lascivious evil and tracing its roots to his earliest days to portraying him as actually not that bad a guy, on the inside, and really he was just corrupted by the evil Catholic church, and he feels really sorry for what he's done, and, and... One could be charitable and say that it's a character study of the effects of evil-doing, but that would be a stretch. Really, it's just an entertaining romp through melodramatic, heinous crimes, with a nice dose of "omg you guys Catholics are so messed up" on the side.
The book is actually tracking two stories, one the story of a young woman named Agnes who falls in love with a very nice young man, but due to a series of unfortunate events (one of them being a pesky ghosts that demands proper burial) is separated from him and placed in a convent. But her lover finds her there and impregnates her, which the Prioress, surprise surprise, does not like that ONE BIT. The Prioress being a monstrous creature, she sets up all kinds of vicious tortures for poor Agnes, as her lover tries to save her. Her lover, conveniently enough, is also her brother's best friend. Which matters, because it provides a link to the second story - these characters know each other!
The second story is of Ambrosius the evil monk and his passion for Antonia - who Agnes' brother is in love with. Ambrosius also matters to the first story, because he is a much respected monk, and part of the Prioress' motivation in punishing Agnes is that she wants to look good in front of Ambrosius. Agnes also pleas with Ambrosius for mercy at one point, and he denies her. She then curses him to seek a similar mercy and be denied, which of course comes true. Lewis reminds us of this a few times, to sort of reenforce the narrative weave - these stories aren't two novels stuck together! They are totally connected!
Anyhow, Ambrosius lusts after Antonia, and becomes an increasingly evil dude in the process. It should be mentioned that before that plot really gets off the ground, there's also a subplot about a young monk that he befriends who - spoiler alert! - turns out to be a woman, Rebecca. They become lovers (Ambrosius' initial fall from grace, though the book can't quite decide to play it that way, and also offers lots of hints that actually, Ambrosius was already too proud of his virtue, and thereby headed for sin), then he tires of her, and she becomes increasingly evil, but also remains loyal to him, which conveniently allows her to do a lot of the heavy lifting in terms of super evil acts. This matters, I think, because it shunts some of the moral weight onto someone else, leaving Ambrosius himself a bit more likable as a character.
Like I said at the outset, the supernatural is kind of peripheral to the text. Yes, there's an actual ghost - which is great, because she enters the text as a ghost story that all these silly superstitious people believe in, and then turns out to be real, and then it turns out that she has some basic demands (bury my body, say some prayers for me) that, once met, get rid of her altogether, and everybody goes back to business as usual. Doesn't seem to be an issue as far as questioning reality goes, despite the fact that the same characters who interact with the ghost are the ones who had earlier pooh-poohed the ignorance of the superstitious. The book also ends with a pretty dramatic otherworldly move (which I won't give away), also kind of a curious choice, in that you'd think the book could just as easily have done without it. But it does have a certain epic satisfaction to it, I have to admit.
But the real terror in the text is entirely human in provenance. It's the evil of Catholicism as an institution, mainly, but more specifically, the evil of a small cast of horrific people. This is an interesting aspect, in that it again calls forth the Gothic's power of social critique. These aren't really novels about ghosts. The supernatural is basically window dressing for this really appalling view of the world, where people are sick monsters who do utterly awful things. Some critics put a kind of rosy spin on this - in his Intro to the book, Howard Anderson writes that "At its best, as in The Monk, the Gothic novel acknowledges that useful warning [of dangers near at hand (as provided by Northanger Abbey)] by expanding our assumptions about where we live to include the dark and frightening regions within ourselves and beneath the familiar relationships to which we look for support."(xvii). Dude, you make it sound like that's a good thing...