Why Is Down Stage Called Down Stage?

Answer 1

If you view a stage from directly above, then the actors movement towards the front of the stage appears as moving "down stage". When theater scenes are choreographed, they are done from a perspective of looking directly down at the stage from above. The same is true when "camera blocking" is done to a film or television scene on a sound stage. Many beginning actors become confused at the direction to "move downstage" or "move upstage", as it is the most commonly corrected stage direction.

Another Answer

Historically, stages were built 'raked', or higher in the back than in the front. This made it easier for the audience, sitting in chairs on a flat floor, to see the action at the back of the stage, or UPSTAGE, which would otherwise be blocked by the actors and set at the front, or DOWNSTAGE.

Stage directions are from the point-of-view of the performer, so on the old raked stages the performer was literally moving "up" or "down" as well as "right and "left."