Don't tell me the moon is shining; show me the glint of light on broken glass.
Chekhov, regarded by many as one of the great writers of the short story, could be talking about a couple of things here. In fact, I'm almost certain he is. First, he's putting another angle on that age-old writing maxim, 'Show, don't tell'. This is a quote I often pull out in my workshops, because it's a perfect way to describe this important idea.
But I suspect he's also saying something about the use of sadness and personal imperfection in our writing. When he was thirty, Chekhov found a new passion and purpose in life: prison reform. His letters and observations from Sakhalin Island penal settlement in far east Russia are graphic depictions of human degradation, and amongst his most moving writing.
There's another Chekhov quote which I really like, but it's got more to do with the way we construct our stories. If the earlier quote is about showing rather than telling, this one is about foreshadowing:
If in Act I you have a pistol hanging on the wall, then it must fire in the last act.