It’s not scary in the modern sense of having shocking graphics, realistic gore, bloody entrails and so forth (there is some of that, but not as much as you’d expect in a ‘modern’ film). No, it’s scary to a thinking person, but in a good way, I think.
It’s good to know about the real horrors that exist in our world, and sharks are one of them. Real sharks can kill real people, and in the way that the movie demonstrates that – with a lot of implied violence – is well done. You won’t see people being eaten, for example, but you will know when it’s happening. You’ll be able to empathize with the victims – and their families. That’s scary enough, right? In that sense it’s more of a “horror” movie, but again, not in the sense that the genre is generally screened these days. (There’s also a certain bland horror in the politics of the thing, too. There was an excellent small example of how horror is done by a small-town politician with an agenda.)
To my mind, one of the scenes of utmost horror was a very calm, almost party-like wholly spoken-word scene among the movie’s three protagonists aboard the boat one night as the skipper recounts an actual horror – this was real-world history – as if he had been a participant. Again, many people might be bored by that scene – it’s just three guys getting drunk on a boat and chatting and singing more or less drunkenly, until one of them opens up about his past (but still “just talking”). It’s only horrible if you listen to what he says and project with empathy. It’s always my favorite part of the film.
See the movie; you’ll enjoy it. You’ll be frightened, and it might be a long time before you swim in the ocean again (and maybe never ever at night!), but how much of that do you do, anyway?
@Zaku has the right of it.
EDIT: And that Onion send-up of the film is fantastic. Simply wonderful. But definitely see the real movie first. And often.