Many of Chekhov's stories deal with loneliness, and the difficulty of communicating with others. In this sense he is a distinctly modern, existential writer. For example, in "The Lament" (sometimes published as "Misery"), a cab driver has just lost his son, and on a cold snowy night tries to communicate this news to his fares, because he desperately needs someone to talk to. But no one listens and at the end of the night he spills his heart to his horse. In "The Lady with the Dog," another famous Chekhov story, a man and a woman carrying on an affair have difficulty putting their feelings into words.
In his study of the short story, "The Lonely Voice," Frank O'Connor has some good thoughts about Chekhov. And if you can, read new translations of his work by Richard Pevear and Larissa Volokhonsky.