The wave period is important in determining the speed with which the waves move across the ocean's surface. There is a formula that says that the wave speed in knots is 3 times the period as measured in seconds. The periods also determine the energy of the waves. 20 second swell waves transport a lot more energy than locally produced seas with a period of perhaps 5 seconds. The wave energy consists of half kinetic energy and half potential energy.
Kinetic energy is the energy of motion and increases with the square of the speed of the waves.
Potential energy is related to the height of the waves or the departure of the agitated surface from the smooth state. The wave speed is however not the speed with which groups of waves propagate across the ocean surface and spread the wave energy from storms to distant shorelines perhaps 3000 miles away. That speed that carries the energy along with it, we refer to as the group velocity of the waves. The group velocity is one half of the actual wave speed. We can therefore take our equation for wave speed or phase velocity in the previous paragraph and use a factor of 1.5 rather than 3 to arrive at the group velocity.