Chekhov's aesthetic of drama, his theory of drama, describes mood as one of the two most important elements in drama, whether tragedy or comedy. To understand this, let's put it in perspective with the standard definition of mood and the standard idea of what is most important is drama.
The standard literary/dramatic definition of mood is that it is a dramatic element that gives the viewer (or reader) a feeling derived from the emotional and psychological aspects of the play. Perhaps the play may be existentially depressed and depressing. Perhaps it may be overwhelmingly tragic and sorrowful. Perhaps a comedy may be lighthearted and joyful. These characteristic feelings are the mood of the play. Additionally, there may be many changes of mood within one prevailing mood. Mood, according to the standard definition, is less important than plot and story-line action: mood only sets the emotional and psychological feeling but plot and action develop the conflict and resolution.
For Chekhov, mood is also defined as the emotional and psychological feelings that are represented and developed in a play, but, unlike the standard definition, mood is more important than plot and action. For Chekhov, it is mood that develops the conflict and resolution. It is mood that drives the plot.
To be more accurate, mood and talking, the dialogue, work together to develop conflict and resolution; to drive plot and action. This is because, for Chekhov, the text (dialogue) reveals the life that is submerged therein, submerged in the text. At one point, Tolstoy is reported to have said that Chekhov's tragedies were not real tragedies because they depended too much upon mood without providing the necessary action that leads to the tragic end.
Act IV illustrates Chekhov's emphasis on mood, first, when Gaev and Lubov are lamenting their lost nursery and cherry orchard and, later, when Fiers lays down on the sofa in despair, ill, forgotten and alone:
GAEV. [In despair] My sister, my sister....
LUBOV. My dear, my gentle, beautiful orchard! My life, my youth, my happiness, good-bye! Good-bye!
FIERS. It's locked. They've gone away. [Sits on a sofa] They've forgotten about me.... Never mind, I'll sit here.... And Leonid Andreyevitch will have gone in a light overcoat instead of putting on his fur coat.... [Sighs anxiously] I didn't see.... Oh, these young people! [Mumbles something that cannot be understood] Life's gone on as if I'd never lived. [Lying down] I'll lie down.... You've no strength left in you, nothing left at all.... Oh, you... bungler!
To summarize, while Chekhov's mood is also defined as emotional and psychological feeling, it differs from the standard definition of mood in that it is more important than plot and action because (1) mood drives the play and (2) mood and talk reveal life.