To exit is to go out of or leave a place. When an actor exits, he moves off the stage and out of sight of the audience.
You can literally exit a room or a building, or exit in a more figurative way: "She decided to exit politics after two terms as Senator." The door or passage through which you exit can also be called an exit, like the emergency exit on a train or airplane. The stage direction, as in "exit, stage left," is the original English use of the word, from the Latin exitus, "a leaving, a going out."