The speaker of "Break, Break, Break" tells us that he can't express his thoughts or his grief, but then he goes on for three more lyrical, lovely stanzas about how much he misses his dead friend. Who says he can't express himself well? So he's probably worried for nothing, but the question of language and communication is still an important one in this poem.
The speaker seems to worry that his attempts to express his grief for his friend will be as meaningless and empty as the "shouts" of the kids at the port or repetitive noise of the breaking waves.
The speaker's longing for "the sound of a voice that is still" suggests intellectual as well as emotional solitude and his desire for conversation with an equal.