I can clearly remember seeing it for the first time: It was showing at our local drive-in and my parents took me with them. I'm not sure how I ended up going.....either my grandparents couldn't babysit, or I begged and pleaded till my Dad relented. The conditions were: 1) no asking questions, 2) no having to get food/drink/go to restroom every five minutes, 3) no talking. They probably figured at five years old, I'd be out cold before the first twenty minutes of the movie.
But they couldn't have been more wrong! The movie grabbed my attention from the opening scene. The movie probably really was too much for me, the concept of water was very familiar to me (I didn't ever really swim in swimming pools when I was little, but we mostly swam at the local lake), and I knew that there were big fish in the water. I didn't really understand the difference between lakes and oceans at five, but I took my parents' word for it that there were no man-eating sharks in the lakes we visited.
So the movie boasts plenty of action, terrifying moments, and got to moviegoers psychologically by taking something so many of us do, and see as relatively harmless (swimming), and reminded us that you never really know what might be lurking just under the surface. This was a movie where the monster was a REAL creature, as opposed to one based largely upon folklore, or a human monster. You can attempt to reason with a serial killer or maybe even the made-up monsters of the classic films, but you can't reason with a shark!
And who can forget the awesome Official Jaws Theme from John Williams?
This movie both scared the bejeezus out of me and excited me, and I credit it with starting my almost-lifelong fascination with sea creatures.