The speaker describes the ocean in two ways: as a calming, unifying presence and as producing the sound of human suffering. Initially, the sea is described in peaceful terms but then the speaker notes that he also hears a violent sound:
Listen! you hear the grating roar
Of pebbles which the waves draw back, and fling,
The speaker compares this roar, an "eternal note of sadness," to Sophocles' Antigone wherein human suffering is compared to the sound of the waves grating on the sand.
Arnold believed that Christianity was dead. In his opinion, there was, therefore, no unifying religious presence with which to unite people in peace. The "Sea of Faith" expressly symbolizes that power of religion to unite people.
The Sea of Faith
Was once, too, at the full, and round earth's shore
Lay like the folds of a bright girdle furled.
But now I only hear
Its melancholy, long, withdrawing roar,
With that power gone, the speaker looks to other places for comfort; namely, his companion/lover. The speaker (Arnold) has lost faith in the unifying power of religion, the calming "Sea of Faith." In its wake, he hears only the roar of human suffering. So, he looks to his lover, with the implication that their love is a substitute power of unity in a world which only "seems" "beautiful" and "new."