Why do you suppose Chekhov ended the play (The Seagull) before the audience is able to witness Irina discovering her son's death?What is the...

Chekhov's style hinges on the idea of all of the big
action taking place off stage.  It's called indirect action, when employed as a
playwrighting device.  Chekhov was less interested in the action itself, but more in the
response to the action.

From the e-notes entry on Chekhov:
 "Although the drama of his contemporaries focused on action, often melodramatic action,
Chekhov’s last plays are primarily works of inaction, works in which the needed action
takes place offstage. Chekhov prevents the audience from being distracted by activity,
focusing attention on the inner lives of his
characters."

By having the action occur off stage, the
audience is allowed to really see into the characters on stage and their reaction to the
off stage action.  In a poorly acted production, this can become deadly, with just a
bunch of talking heads on stage.  But, in a well-done production, it can be more
exciting than you might imagine.  Actors have the task of uncovering the subtext and
finding outward expression for it; in a good actor's hands (and with a good director
leading), this is marvelous to watch.   Chekhov wrote plays that very much fit the
approach of Stanislavski (founder of the Moscow Art Theatre, acting teacher, director),
whose techniques allowed the inner lives of Chekhov's characters to be
revealed.