Jaws is a classic multi-genre film. Its legacy is so enduring in part because it does each so well. It is, first and foremost, a film of adventure on the high seas. That's the way Stephen Spielberg thought of it, anyway. Composer John Williams agreed with him, and modeled much of the film's score on old-fashioned swashbuckler movies.
There's also the strong horror element. It's a monster movie extraordinaire, and much of the audience's enjoyment comes from the tension, terror, and tragedy of each shark attack. Jaws has been compared to Hitchcock's greatest thrillers, such as Psycho and Vertigo, and even borrows many elements from these films.
You can also see Jaws as a quasi-political thriller. The moral compromises made by the citizens and leaders of Amity Island, chiefly Mayor Vaughn, pit Chief Brody against a corrupt system that he's unable to overturn until it's too late.
Finally, Jaws—particularly the last act—is about a quest: Three men set off to hunt a monster, each equipped with a special set of skills; each burdened by weaknesses that may doom them all if they can't band together. There are "buddy film" qualities in the quest—very different guys who start out competing with each other but end up respecting and caring about each other.
Any one of these stories-within-the-story would be exciting enough in its own right, but when combined so seamlessly by Spielberg, the result is the granddaddy of all blockbusters—which in a way is a genre unto itself, too (source).