There are different types of show: reality shows, horse shows, light shows, quiz shows, TV or radio shows and late night shows. One is certain: the show must go on. The other one is certain, too: you must steal the show. Always. (=be the one most visible, best remembered, most vivid!)
Definition: to make others pay attention mainly to you.
Example: Lerni was absolutely brilliant in this play. He stole the show!