Sea Ice is a very important factor in deep ocean circulation and deep ocean circulation is thought to be an important factor in the long term climate of the earth. At high latitudes salinity is the main determinate of sea water density. As sea ice is growing, salt is rejected from the ice. The salt then mixes with the sea water underneath the ice layer. Because of this ice-rejected salt, the water directly beneath the ice is very saline and thus has a high density. In addition to having high salinity, the water is cold. In the ocean, cold, dense water is convected downwards to great depths (see picture below). This convection is what in part drives the deep ocean circulation. If the deep ocean circulation were to stop, for instance, because there was no cold, dense water from sea ice, areas in the North Atlantic would have drastically different climates. 

The climate of much of the North Atlantic is warmed because deep ocean convection, as described previously, occurs there. The cold waters in the North Atlantic sink to the bottom and are replenished with warmer waters from the North Atlantic Current. These warm waters mediate the climate of the North Atlantic and without them the temperatures would be much colder (See above Figure).
In addition and perhaps in opposition, sea ice reflects more sunlight than the open ocean leading to further cooling in areas of large sea ice coverage. Sea Ice also insulates the ocean from heat loss.
The role of wave-sea ice interactions in all of this is that waves contribute to ice growth and in some cases to the melting of sea-ice. So in order to understand the climate processes it is helpful to understand the dynamics of the ice. Wave-sea ice interactions are one facet of ice dynamics.