The speaker is telling the ocean waves to "break," but we don't realize that until the second line where he finishes the sentence. As we first read the poem, we just see this word "break" repeated three times. It's not a happy word – we break bones and hearts and vases. The word itself is a harsh word, with that "br" sound at the beginning and the hard "k" sound at the end. And the repetition, with the commas in between, "breaks" up the line, suggesting the speaker's "broken" heart…you get the picture.
On thy cold gray stones, O sea! (2)
The repeated long "o" sound (in "cold," "stones," and "O") sound almost like moaning. And "cold" and "gray" surroundings are almost always setting the scene for something sad.
That he shouts with his sister at play! (6)
The children of the fisherman seem unaware of the deep grief of the speaker as they play around happily.
As he sings in his boat on the bay! (8)
The "sailor lad," too, seems totally oblivious of the speaker's sorrow – he's singing away like he doesn't have a care in the world, because he probably doesn't.
But O for the touch of a vanish'd hand, And the sound of a voice that is still (11-12)
The speaker breaks down and expresses his longing for the presence of his dead friend beginning with that moaning "O." The conjunction "But," with which he separates his own sad longing from the business of the "stately ships," suggests how out of sync his sorrow is with the busy activity of the rest of the world.
But the tender grace of a day that is dead Will never come back to me. (15-16)
The speaker realizes that time goes on, and he'll never be able to relive the days that he spent with his dead friend.