What message, moral, or universal truth is revealed in "The Lady with the Pet Dog" by Chekhov?

The affair between Dmitri and Anna began because they were both bored and because they were both unhappily married. Dmitri didn't really understand his feelings until he got back to Moscow and resumed his normal routine. One night he tried to describe his affair to a friend, but the other man couldn't understand him. As he was getting into his sledge, the friend said, "You were right this evening: the sturgeon was a bit too strong."

These words, so ordinary, for some reason moved Gurov to indignation, and struck him as degrading and useless. What strange manners, what people! What senseless nights, what uninteresting, uneventful days! The rage for card playing, the gluttony, the drunkenness, the continual talk always about the same thing. Useless pursuits and conversations always about the same things absorb the better part of one's time, the better part of one's strength, and in the end there is left a life grovelling and curtailed, worthless and trivial, and there is no escaping or getting away from it—just as though one were in a madhouse or a prison.

This insight motivates Gurov to seek out Anna again. But they have both made irrevocable choices in the past and cannot break free from the lives that have evolved as a result of their previous choices. The best they can do is to see each other for a few days every two or three months. Would they have been better off if they had never met? Would it have been easier for them to put up with their "worthless and trivial" routines? Characteristically, Chekhov does not provide an answer.

Many readers can identify with Gurov and Anna because they too feel they are stuck with "a life grovelling and curtailed, worthless and trivial, and there is no escaping or getting away from it--just as though one were in a madhouse or a prison."

What is the main idea of "The Lady with the Dog" by Anton Chekhov?

One of the characteristic motifs of Anton Chekov is that of Communication.  This problem with communication often exists when different social classes mix or when people misunderstand the intentions of others.  Such is the case in Chekov's story about an effete aristocrat who dallies with women, whom he terms "the lower breed," simply to amuse himself and relieve his ennui.  His conflict arises when he realizes that the unpredictable has happened in his tryst with Anna Sergeyevna:  He falls in love with her.  But, this love is doomed since he and Anna are both married.

Likewise, Anna Sergeyevna, who is unhappy and dissatisfied in her marriage, believes that she can find some joy in her relationship with Dmitri Dmitritch Gurov.  However, she misunderstands Gurov's intentions at the first; then, she is haunted by her belief that he does not respect her.  When Gurov, having realized his true feelings, seeks her in her own town, they both realize that their personal lives rest upon secrecy and their love for each other has irrevocably changed them because of their unpredictable stituation: "But how far they were still from the end!"  Certainly, with both Gurov and Anna, their memories of the past are powerful parts of any present moment, and they are, thus, tragic figures in their search for meaning since no true, lasting communication can exist between them.

As many of his stories do, Chekhov's story ends on a note of ambiguity.  For, the lovers realize that

they had still a long, long road before them, and that the most complicated and difficult par of it was only just beginning.

Anna and Dmitri must both find ways to communicate with each other while living their separate lives as well.