I assume you used a slow shutter speed?
Yes. During the time that the shutter is open, the waves continue to move. Instead of looking like waves, they look more and more like fog or mist. You often see a similar effect with waterfall pictures. Shorter exposures show the fall frozen in time. Longer expsures show a soft sheen of where water has moved during the photo.
There are several interesting effects that can be achieved during a long exposure. You can have a person in one place during part of the exposure and then gone for the rest. In that case, you'll see them and what's behind them, makin them look like a ghost.
Objects that are much brighter than the rest of the subject, such as a flashlight, sparkler, or a candle, can be moved while shooting the picture. In those cases, they appear like lines and curves in the photo. A classic example of this is long exposure photographs of roads where the headlights and tail lights leave trails of white and red lines across the picture.
Another fun thing to do during a long exposure is to paint with light. If you take a picture of a dark scene and, during the exposure run around painting objects in the picture with a flashlight, those objects will show up much brighter than everything else.
As I said before, very long duration photos showing the night sky record the trails showing the paths of the stars across the sky.
Long exposures on dark stormy nights are a great way to capture lightning bolts.
You can also pan the camera during long exposures to track a moving object. When done well, the subject is sharp and the background has a motion blurred look to it, emphasising the speed of the subject. Some image stabilizers have a mode that forces them to stabilize motion perpendicular to the panning direction but not to mess up the panning. Personally, I've gotten better results for most motion shots by using a high shutter speed to freeze the action, cutting out subject, applying motion blur, and then pasting the frozen subject back on. Panning well is really, really hard. Cut-blur-past in Photoshop is easy. See my kids sledding in the cold weather picture thread for an example.
Finally, if you are using a camera that can do it, mixing flash and long exposures can help get some great shots. Let's say that you want to take a picture of your special person in front of the castle during the fireworks show and you want to capture a bunch of fireworks. Typically when you try to do this you either get a quick flash shot which shows few if any fireworks or a great fireworks shot with a blurry person that wasn't perfectly still during the 5 second exposure. What you can do is set up the shot to capture the fireworks and castle but ALSO fire the flash to illuminate the person. Most of the light for the person will come from the flash, so if they move a bit, it won't show. The long exposure will give time for the background to appear.