What are stage directions?

Stage directions are directions given to the actor(s) by the director. They involve the physical movement of the actors on stage. The actors are supposed to note the directions in their scripts. The Stage Manager is also supposed to write down all stage directions in their master book, known as the "Prompt Book". If there is any disagreement about where an actor is supposed to move, or how, the prompt book is the final word. If the director does not like the movement, or changes his mind, the prompt book is revised.
Terms:
Upstage: moving away from the audience, towards the back of the stage.
Downstage: Moving towards the audience, towards the front of the stage.
Stage Right: Moving towards the Right (facing the audience)
Stage Left: Moving towards the Left (facing audience).
Cross: Crossing the stage to a predetermined position.
An example in a prompt book might look like: "X(cross) DSL to DSC (down stage center), X US (upstage), and out (exit) SR (stage right).
The above is just a few major terms. There is a different notation used choreography is being notated.