The setting of Matthew Arnold's "Dover Beach" reflects both his personal situation and poetic aethetics. On a personal level, Matthew Arnold is reflecting on an unsuccessful relationship with a woman in France from whom he is now separated by the English Channel; his poem "To Marguerite" also discusses this relationship.
On a metaphorical level, the setting operates in several ways. First, the external world reflects the mood of the narrator (Wimsatt calls this the "pathetic fallacy"). The sea, which like faith, once encompassed the entire world is seen as receding, and the ebbing of the tide seems to the narrator to call forth a sense of the disappearance of the old certainties of belief. The darkness of the night and the gleam of light in France also are allegories for the state of knowledge.