Waves on water are perhaps the most familiar example, but sound and light also travel in waves.
Waves carry energy from place to place and can also transmit information.
It is easy to generate a wave. If you throw a stone into a large, still pond, a series of disturbances will travel outward from the point where the stone enters the water. Energy produces the disturbances, and the disturbances carry energy. As the stone penetrates the surface, energy carried by the stone displaces some water. The water closest to where the stone entered rises and then falls, producing a ring-shaped disturbance with the stone's entry point at its center.