In the world of "Harrison Bergeron," everyone is equal. To achieve this extreme equality, people must wear "handicaps." For example, someone who very strong must wear weights that slow them down and tire them out. Someone with good vision must wear glasses that prevent them from seeing well. In this way, no one is better off than anyone else. Everyone is truly "equal."
Harrison Bergeron, however, refuses these handicaps. He is strong, smart, and very good looking. He must wear many handicaps that attempt to make him equal to everyone else. At some point, he refuses to wear them any longer.
When Harrison enters the TV studio, he declares himself "the emperor" and removes all of his handicaps. This is a shocking act for viewers to see. He commands a ballerina to remove her handicaps and join him as his empress. When she removes her handicaps, she is beautiful as well as graceful. At this point in the story Diana Moon Glampers, the Handicapper General arrives and kills Harrison and the ballerina.
Harrison's death is significant because it proves that extraordinary people cannot survive in this type of society. His death is necessary for this society to continue.
In fact, if Harrison were not killed, others might believe that they too could remove their handicaps. Harrison had to die for the sake of this "equal" world. Had Harrison been allowed to continue without his handicaps, others would have followed. It would not take long before everyone removed his or her handicaps, and no one would be "equal" any longer.