He’s the father of “Show don’t tell.”
Every major short story writer of the 20th Century studied him very closely. Most emulated him.
Chekhov’s Gun: The gun on the wall in Act I must go off by Act III. No extraneous details.
Less emphasis on plot, more emphasis on the main character’s internal consciousness (i.e., her/his fears/desires/motivations/impulses/etc).
Many of the “tenets” of “literary” fiction that we take for granted in workshops (etc) come directly from Chekhov and/or someone who really, really liked Chekhov.
Also, it must be noted, Chekhov wrote hundreds of stories. He wasn’t above ignoring/bending these “rules” in a few of them. That doesn’t make said rules less useful, true, or influential.
WHAT CHEKOV SAID ABOUT WRITING
“My own experience is that once a story has been written, one has to cross out the beginning and the end. It is there that we authors do most of our lying.”
“Another piece of advice: when you read proof cross out as many adjectives and adverbs as you can. You have so many modifiers that the reader has trouble understanding and gets worn out. It is comprehensible when I write: “The man sat on the grass,” because it is clear and does not detain one’s attention. On the other hand, it is difficult to figure out and hard on the brain if I write: “The tall, narrow-chested man of medium height and with a red beard sat down on the green grass that had already been trampled down by the pedestrians, sat down silently, looking around timidly and fearfully.” The brain can’t grasp all that at once, and art must be grasped at once, instantaneously.”
“In my opinion it is not the writer’s job to solve such problems as God, pessimism, etc; his job is merely to record who, under what conditions, said or thought what about God or pessimism. The artist is not meant to be a judge of his characters and what they say; his only job is to be an impartial witness.”