In the ocean, waves occur when wind pushes against the surface of the water. Water molecules pushed forward by the wind at a certain point push against the molecules in front of them, and so on. The collective pushing of all those molecules results in waves.
Creating waves artificially in a relatively small, contained body of water works on the same basic principle. Something is used to push on the water at the deep end of the pool to create waves. Most serious wave pools use a reservoir system that uses huge amounts of stored water to create the necessary push.
Reservoir pools have four basic parts: a water pumping system, a reservoir to hold the water, release valves at the bottom of the reservoir, and a canal at the shallow end of the pool to return water to the pumps. The pumps draw the water into the reservoir, which in large wave pools can hold up to 90,000 gallons. When the reservoir is full, the release valves open, dumping the water into the calm, motionless water of the pool. The sudden influx of so much water, like a strong wind, pushes the pool's water forward, creating a sizeable wave. When the wave washes up at the front of the pool the canal channels the extra water back to the pumps, and the process begins again.