In the world of Harrison Bergeron, the government has made every attempt to make every person equal. Personal strengths and personal assets are diminished through the use of the handicaps. Because Harrison is a gifted athlete -- very strong and fast, as well as being very smart, he has many handicaps added to his physical self so that he can't be smarter, stronger, or faster than anyone else. When he breaks through the buzzing in his ear that disturbs his thought processes he realizes the ridiculousness of the handicapping system. His shedding of the handicaps is symbolic of his becoming true to himself and his abilities. The theme of story is that while all men and can and should be treated equally, it is not possible for all people to be perfectly equal. Every person has their strengths and weaknesses and that is what makes life interesting. The diversity of people's strengths and interests is what makes society function in its most productive way. While handicapping people may make some people feel better about themselves (no one is prettier, no one is smarter etc.), it destroys the human potential of each person. Without potential, the human race will never progress and achieve new advancements. When Harrison sheds the handicaps he is attempting to reclaim his humanity and his individuality -- the things that make him unique!
Vonnegut was always critical of the many ways that men and women were limited by the systems around them whether that was the government or industry or propaganda in the form of news, etc. In this future version of America, those systems have all been made to work together in the form of TV broadcasts, the handicapping system, and the enforcers of those handicaps.
So when Harrison emerges on the screen and tears off all of his handicaps, it represents a blatant and violent challenge to these systems of control. Vonnegut is using Harrison as a symbol of what he believed to be a human and/or American desire to excel to be powerful and strong and rise above mediocrity.
Harrison serves as an illustration of the power that talented and capable individuals have to push back against those who would use various means to try and forcibly make everyone equal.