Name of text describing an action in a play

Stage direction — as mentioned in The Free Dictionary.

When the play is actually staged, as StoneyB says:

The action itself is called business in The Profession, unless it involves movement from one location to another, when it is called a cross, verb to cross. All business and crosses together constitute blocking; the director (producer in GB) blocks the play, with as much or as little fidelity to the writer's stage directions as he likes.