Another perspective on Matthew Arnold's "Dover Beach" involves thinking about the actual geographic setting that Arnold is focusing on, and the symbolic significance of what he sees (or doesn't see).

Dover Beach is located on the southeastern coast of England. The European continent lies to the south/southeast of it. Arnold references this in lines 3-4 by writing "on the French coast the light/ Gleams and is gone." While this is a reference to a specific area, the light is also symbolic of the light of knowledge and progress, of new ideas entering into the world. In this way, Arnold's work takes on a somber tone as the light disappears. The tone is carried on as the narrator finds himself isolated as lines 12-14, describing the motion of the waves which

Begin, and cease, and then again begin,
With tremulous cadence slow, and bring
The eternal note of sadness in.

Stanzas two and three expand on this idea, referring to Sophocles hearing the sound "of human misery" and the following discussion of the Sea of Faith, which

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,

Retreating, to the breath

Of the night-wind, down the vast edges drear

And naked shingles of the world.

This is a poem that starts out sounding like a nice poem about nature and maybe love.  But it soon turns to one in which the poet is really showing despair about the way the world is.

In the first part of the poem, the speaker is just enjoying the sights and sounds of the sea.  He tells his love to listen to the sounds.

But then he thinks about how this same sound had made Sophocles think of how much people suffer -- how their lives are sort of tossed around by the waves like the pebbles.

So then the poet starts thinking about how Christian faith used to tie everyone together the way the ocean does.  He is sad that the world is not like that anymore.

He hopes that love will help make sense of this world, but he ends the poem on a down note -- he thinks that nothing can really fix the confusion and pain of the world.

You will find two good explanations of the poem in the links below.