When Harrison Bergeron escapes from jail, he shows up on the set of the television production currently being aired live. He is wearing all his handicaps, which makes him look like a walking junkyard. In front of the viewers, he sheds all his hardware, removes his glasses and clown nose, and selects a ballerina to be his Empress. He removes her handicaps as well. He then addresses the orchestra, removes their handicaps, and commands them to play better music. When they begin playing "cheap, silly, false" music, he picks a couple of the musicians up and waves them in the air "like batons."
At this point, we can see the action of the story is becoming more unbelievable. For a man to be able to pick up two other men and wave them in the air like batons would require superhuman strength, yet we have been told that Harrison "would have awed Thor."
As Harrison begins to dance with the ballerina, the hyperbole continues. They defy "the law of gravity and the laws of motion" as they ascend thirty feet high and kiss the ceiling.
The point of the dance is to show the unbounded potential of human achievement when people are allowed the freedom to be themselves, operate in their strengths, and follow their passions. By making everyone equal, Harrison's society has tethered its citizens to the ground, preventing them to reach the heights of which they are capable. The dance is the contrast to the society; it represents what life could be and should be without draconian governmental interference. It inspires readers to leave behind whatever is holding them back and have the courage to be who they are.
Near the end of Kurt Vonnegut's short story, "Harrison Bergeron," Harrison does the unthinkable in a society where everyone is forced to "be equal in every way." Since he is physically beautiful and strong and also very intelligent, Harrison has been weighed down with all kinds of handicap contraptions, both physical and mental. When he hears the musicians playing mediocre music and sees the ballerinas trying to perform despite their handicaps, he becomes very angry. Harrison rips off his handicaps, orders the musicians to play better and relieves one of the ballerinas of her handicaps, so that they can dance together. They leap higher and higher, becoming freer and freer.
The significance of the dance is that it symbolizes freedom. Not only are they free of their handicaps, but they are free in every way if only for a very short period of time. Harrison shows the world what it is like to be his true self in, perhaps, the hope that others will follow. He would rather die free than live in a society where he is not free.