According to wikipedia, the restoring force of water waves are gravity or surface tension, depending on the wave length and water depth. I can't understand exactly the gravity explanation.
If gravity was the sole restoring force, the result could be a local temporally oscillatory movement, like a pendulum.
I can't see it as a source of a propagating wave.
There are compressive waves as sound, or seismic waves. Or tensile waves that happens in a string or a membrane.
In all that cases, it can be understood why an initial movement propagates.
I understand water waves as a side effect of pressure waves, but I'm not sure if it is right because they are not usually explained that way.
For example: a stone is thrown in a lake. There is a local sudden pressure increase. As a consequence, the level of water increases near the event, (because the atmospheric pressure is constant). The pressure wave in the water propagates to all directions, including upwards, leading to concentric circles that we see spreading at the water surface.