Walter De La Mare's poem "The Listeners" deals with a lone stranger who is searching for a clue as to where everyone has gone.
The wave image at the end of the poem refers to the fact that everyone leaves something behind. Think about how a wave crashes upon a beach or rocks. The water the wave has hurled upon the rocks or beach never completely retracts. Instead, some of the water remains behind.
Another way to look at the imagery of the wave is the fact that the power of a wave can change the landscape of objects it comes in contact with.
Therefore, the waves, in the poem, are used to represent the fact that people have been in the home the unknown traveler is standing near. He knows that people have been there and he calls out to them, unsure of what he may come to find. Regardless of his uncertainties of what may come from his cries, the stranger is certain that "listeners" are there--much like the water left by waves which have crashed upon the shore.
One last way to regard the imagery of the waves is the fact that once the stranger leaves the house becomes silent again. The coming of the stranger rang out on the silence like the hooves of horses given the house has certainly been enveloped in silence for a long time. As the stranger walked away, "the silence surged softly backward," the sound of his footsteps, "the plunging hoofs," disappeared as well.