What do the clouds, the grasshoppers, and the sea together represent or symbolize in Chekhov's "The Lady with the Pet Dog"?
"Yalta could be dimly discerned through the morning mist, and white clouds rested motionless on the summits of the mountains. Not a leaf stirred, the grasshoppers chirruped, and the monotonous hollow roar of the sea came up to them, speaking of peace, of the eternal sleep lying in wait for us all. The sea had roared like this long before there was any Yalta or Oreanda, ...." (Chekhov, "The Lady with the Pet Dog")
The passage you refer to, added as a quote below your question, is an important pivotal passage in one of the most important paragraphs of the story. In this paragraph, Chekhov offers his metaphysical solution to the moral dilemma Anna faces in the story (essentially, the indifference of the sea represents the indifference of life and death to human action thus there is no moral dilemma). The passage in question acts as the pivotal transition between the narrator's (Chekhov's own voice) focus on Anna and Gurnov to the narrator's focus on metaphysical contemplations.
white clouds rested motionless on the summits of the mountains. Not a leaf stirred, the grasshoppers chirruped, and the monotonous hollow roar of the sea ... speaking of ... the eternal sleep lying in wait ....
In this transitional passage the three natural elements, clouds, grasshoppers, and sea symbolize the spiritual devastation Anna's violation of her beliefs has caused her to feel: "I am a bad, low woman; I despise myself ... I have become a vulgar, contemptible woman ...." The only sounds are the grasshoppers and the sea; nothing shows any sign of life, not even the clouds that hang in the air. They also symbolize the loss of momentum her life has suffered because she went against her life's previous motivation, Russian Orthodox belief: nothing moves, no leaf, no cloud, not even the morning mist.
They also symbolize Anna's sense of inner death after her "fall" ("very grave, as though it were her fall") and Gurov's feelings of disconnectedness ("a regular problem of extreme intricacy ... the situation becomes unbearable"). In this symbol, the sea has a "hollow roar," sounding of emptiness and death: "monotonous hollow roar of the sea [speaking] of the eternal sleep lying in wait ...." This symbolism ultimately provides the pivot, via the metaphysical description of the sea, to introduce Chekhov's metaphysical speculations about the solution of Anna's moral dilemma.