Energy is transferred in electromagnetic waves by vibrations in electric and magnetic fields. The vibration of air particles is energy transfer in sound waves, while the transfer of energy in water waves is the oscillation of water particles.
When a water wave, a transverse wave, approaches the shore, the water particles are not moving in the same direction as the wave, they are moving perpendicularly to it, hence the characteristic peaks and troughs that people see. Water particles in the wave bump into each other and transfer energy, causing the up-and-down motion. A Mexican wave at a soccer match is a good analogy for this motion; spectators simply stand up and sit down but the wave travels around the stadium.
The up-and-down motion of a wave shows that kinetic energy (movement energy) has been imparted to the water particles. As the water particles move toward the wave's peak or trough, some of their kinetic energy is converted to potential energy. Particle energy in a wave swings between potential and kinetic energy.
The farther away a wave particle is from its normal position, the more potential energy it possesses. This explains why a tsunami is so destructive. As the wave approaches the shore, it gains in height, so it contains more potential energy. When it impacts with land, that potential energy is converted back into kinetic energy.