Although the elegy originated as a very formal (in meter and rhyme scheme) lament for the loss of a friend or an important public or cultural person, in its broader sense, the elegy also laments the loss of something important to the world. In "Dover Beach" (1867), Arnold writes about the loss of faith in the world at large.
The poem begins with very positive images:
The sea is calm tonight./The tide is full, the moon lies fair/Upon the straits . . . Come to the window, sweet is the night air!
These conventionally pastoral, peaceful images establish an initial positive tone, but in the fifth line, Arnold's tone shifts dramatically and ominously:
Only, from the long line of spray . . . Listen! you hear the grating roar/Of pebbles which the waves draw back, and fling . . . The eternal note of sadness in. (ll.7-14)
The diction moves from the peaceful "sweet is the night air" to the harsh "grating roar/Of pebbles," signaling Arnold's shift from pleasantries to something ominous.
That the poem is about the loss of something important is made clear in the second stanza's reference to Antigone and Sophocles' awareness of the "turbid ebb and flow/Of human misery" (ll.17-18). Arnold points out that just as Sophocles "heard" human misery on the Aegean Sea, we hear it "by this distant northern sea," which is to say that human misery is everywhere and timeless.
The fourth stanza makes explicit the loss of faith, faith that used to encompass the world "like the folds of a bright girdle furled" and now, like the tide, "retreating . . . down the vast edges drear/And naked shingles of the world" (ll. 23-28). In other words, faith once encircled the world (a "Sea of Faith"), but now, one only hears it as it leaves the world "naked," that is, without faith.
Given the world's loss of faith, Arnold suggests in the final stanza that the only solace is found in the love of two people:
Ah, love, let us be true/To one another! for the world . . . Hath really neither joy, no love, nor light,/Nor certitude, nor peace, nor help for pain. . . . (ll. 29-34)
Arnold argues here that the world--in which faith as a guiding force is dead--can no longer provide any sustenance to the individual, and to the extent that comfort can be achieved, it will be found only in an individual's love for another.
The last three lines--the most quoted in all of Arnold's poems--make it clear that the world, which he describes as a "darkling plain" on which "ignorant armies clash by night," is beyond redemption, beyond hope, beyond faith--no longer a place where love can thrive.