A beat is an old term used by most other actor training systems that comes from Stanislavski's use of it at the Moscow Art Theater. It is basically a moment in the script where something happens, characters come in or go out or something causes your character to do something. Often a beat is marked by a pause.  It essentially breaks down the script (and story) into the smallest atom. And these atoms of text are subjective - it might be obvious in the text, but it is often not and is something the director will point out to you.
In Chekhov work, we know about beats, but they aren't too important to us. We do mark anytime something in the text or directions causes an atmosphere change. That might be when a major character enters or exits. Or it might be when something in the flow of the story happens (like a major event) that affects everyone in the play. To use this, you need to understand overall and personal atmospheres, so go back to Joe Herrera's videos to learn more about atmospheres.
Whether you use beats or events (which is what we call climaxes, which we count 9 in a play or film of any length), it's important because it provides interesting moments in the story. The audience sees these beats or atmosphere changes as important signposts in the story. And they help you as the actor to know where you are and how to change your character's "feelings" or actions as a result of it.