The Question and Answer section for Kurt Vonnegut’s Short Stories is a great resource to ask questions, find answers, and discuss the novel.
The idea is that, if everyone were equal, nobody would take advantage of anyone else. People would not fight and there would be peace and harmony. Unfortunately this comes at the expense of individuality and the human spirit.
The government has made everyone the same by "handicapping" them. If they are too intelligent, they have equipment that disrupts their thought patterns. If they are too "good looking" the government makes them wear masks: too strong; they wear...
In Harrison Bergeron, society controls the thoughts and actions of people. They "handicap" people, like George and Hazel, to think at a very elementary level. This greatly impedes people having different ideas that might challenge the government.