Most of the waves are wind driven. As the wind blows across the ocean it pushes against the surface. This creates a small hump. Which presents a larger area for the wind to hit, imparting more energy and growing the wave.
The waves move because thats the direction the initial force that created the wave was moving. The wave is a transfer of energy. Water has very little internal friction, so these waves will continue long after the wind that created them stops. The do spread out as they travel though. This spreads the energy over a wider area resulting in the wave becoming smaller.
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