To upstage is to steal the show. If you try to upstage your Grease costar, you'll attempt to pull the audience's attention away from him and onto you at the back of the stage doing cartwheels.
A child actor might accidentally upstage an adult simply by being adorable, or a minor character could upstage the star of a play with an amazing performance. When you upstage someone, the audience's focus shifts from that person to you. Another way to use the verb upstage is to describe the acting technique of moving back on the stage, away from the audience, so that another actor must turn her back toward them.