The sea is calm to-night.
The tide is full, the moon lies fair
Upon the straits; -on the French coast the light
Gleams and is gone; the cliffs of England stand,
Glimmering and vast, out in the tranquil bay.
Come to the window, sweet is the night-air!
The "straits" are the narrow channel between England and France, at Dover Beach in the southeast of England. This is where the poet, presumably from the window of a house or inn overlooking the sea, is looking out towards the beach at night. This is not a tropical or sandy beach; it is rocky, and the moonlight is reflecting off the famous white cliffs of Dover. While the straits are an enchanting image, it is the beach itself which is important. Possibly the dimly-seen shore of France could represent the desires of humanity for the divine; but this seems a bit of a stretch.
So the "straits" themselves, which is simply the narrow channel, is not what is important to the poet. It is the view of the beach, and, specifically, the movement of the waves on the beach, which has larger significance to him.
The poet goes on to show how Sophocles had found the futility in human life expressed in the constant motion of waves hitting a beach. This is a desolate "rasping" sound, and does not evoke the sometimes calming or meditative emotions that the motion of waves on a beach create for many people today. Arnold hears the sound and thinks of the futility of the motion, and its age-old pattern of individual waves breaking, and having their death (like every human being since the beginning of time) on the rocky beach. Each wave is slightly different than the other, and has a slightly different effect on the pebbles of the beach, but every wave, like every human life, is ephemeral, and any effect it has is quickly obliterated by the wave that follows it.
This existential crisis is coupled with another ocean metaphor; that of the Sea of Faith (line 21) which
Was once, too, at the full, and round earth's shore
Lay like the folds of a bright girdle furl'd.
But now I only hear
Its melancholy, long, withdrawing roar,
Retreating, to the breath
Of the night-wind, down the vast edges drear
And naked shingles of the world.
Arnold is further depressed by the thought that not only is human life like an ephemeral and death-bound wave, but the Sea of Faith, which once girt the world with its comforting influence, is receding from humanity at an alarming rate. This means, to Arnold, that not only is the brevity and fragility of human life frightening and distressing, but humanity no longer has the comfort of faith in God anymore to assuage it. This is how Arnold comes to the humanist idea of creating meaning in human life by focusing on human love:
Ah, love, let us be true
To one another! for the world, which seems
To lie before us like a land of dreams,
So various, so beautiful, so new,
Hath really neither joy, nor love, nor light,
Nor certitude, nor peace, nor help for pain;
And we are here as on a darkling plain
Swept with confused alarms of struggle and flight,
Where ignorant armies clash by night.
While the image of the meaningless waves crashing on the beach has reduced the poet's vision of his own, and others', lives to a futile brief struggle, he clings to the idea that only true human love and faithfulness can give meaning to human life. The effect of each life is essentially nothing, and there is no God to cling to any longer (he says), so we must find our meaning in each other.