"The Lady with the Dog" is famous for breaking the rules of what a short story should be. As author Vladimir Nabokov said of this work in his Lectures on Russian Literature, "There is no problem, no regular climax, no point at the end. And it is one of the greatest stories ever written."
Consider the story's conclusion: "It was clear to both of them that they had still a long, long road before them, and that the most complicated and difficult part of it was only just beginning." The last word is "beginning." Chekhov isn't wrapping this up with a bow; he's essentially leaving it unfinished. Part of this has to do with Chekhov's own ideas about what a story should do, namely ask questions instead of answering them. We talk about this a lot more in "What's Up With the Ending?", so be sure to check that out.