I think the quote that summarizes the story of "Harrison Bergeron" is from The Declaration of Independence":
"We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, --That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness. Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes; and accordingly all experience hath shewn, that mankind are more disposed to suffer, while evils are sufferable, than to right themselves by abolishing the forms to which they are accustomed. ...it is their right, it is their duty, to throw off such Government, and to provide new Guards for their future security."
Harrison Bergeron and his Ballerina were standing up for what the Declaration says and they were exercising their right to change a terrible government that took away the precious rights we have which are guaranteed by the Declaration.
"THE YEAR WAS 2081, and everybody was finally equal. They weren't only equal before God and the law. They were equal every which way. Nobody was smarter than anybody else. Nobody was better looking than anybody else. Nobody was stronger or quicker than anybody else. "
The reason this is such a well put quotation is because this is what the society is about, equalizing all of its members. If someone is beautiful he or she is forced to wear an ugly mask. If someone has above average intelligence he is forced to wear some device that makes him mentally handicapped. Harrison was born virtually perfect for this society so he was arrested and made to look like a freak.
"All men are Not Created Equal and it is the duty of the Government to render them so". This is the essence of the story, the pinnacle of the plot. I use this statement to describe the story to those who've never heard of it.