Listen! you hear the grating roar
Of pebbles which the waves draw back, and fling,
At their return, up the high strand,
Begin, and cease, and then again begin,
With tremulous cadence slow, and bring
The eternal note of sadness in.
Sophocles long ago
Heard it on the Aegean, and it brought
Into his mind the turbid ebb and flow
Of human misery; we
Find also in the sound a thought
Hearing it by this distant northern sea (lines 9-20, Wain 455-6)
Matthew Arnold is talking, to his beloved, about the sound of the waves on Dover Beach. The small pebbles are being flung back and forth by the waves, and Arnold recalls that Sophocles had found in this sound a reminder of the "turbid ebb and flow of human misery". The sound of waves, in their ever-changing but essentially pointless repetition call to the poet's mind the futility of human life and activities. Since this poem is about the loss of faith and humanity's search for meaning this sound is a metaphor for the lives of human beings.
Each wave that hits a beach is different from every other wave. Though there are many similarities in the pattern and effect of each wave, the exact force and amount of water vary enough to make every wave unique. This can be likened to human lives (which all share the commonalities of birth, life, and death) in that each life has the same destination, but how it gets to that destination varies from every other life. Likewise, the number of pebbles tossed by each wave is different, and the exact pattern of the pebbles varies every time. But every life ends in death, as the end of every wave is its dissolution on the shore. Arnold finds this thought depressing, in that even if each life, like each wave, is unique and has a different effect on the beach (by the difference in the pebbles it leaves) any effect is impermanent and is washed away by the following waves. It is this pointlessness of the uniqueness of lives, and the impermanence of any mark left by those lives that causes Arnold to bewail the loss of Faith.
In the following stanza Arnold extends the metaphor by saying that the "Sea of Faith" once girt the world. Since it does no longer, Arnold says, human beings must look to each other for the meaning once supplied by religion. Arnold turns away from the hopelessness of Sophocles' image of "human misery". Arnold reminds himself (and his beloved) that the world is a "darkling plain" in which the things that seem "So various, so beautiful, so new" are meaningless. Arnold turns away from the theism of the past to a humanism of the future.
Source: Wain, John, ed. The Oxford Anthology of English Poetry Volume II Oxford: Oxford University Press, 1990.