Pretty much everyone in the future society depicted in the story has some sort of artificial handicap, from heavy weights to ugly masks. This prevents anyone from excelling at anything (for example, one actress being picked over another for her looks), and so ensures that everyone is "equal," at least physically and mentally. George, Hazel's husband, has a mental handicap that plays loud noises to distract him and prevent him from thinking about things. While it is likely that Hazel has some physical handicaps:
Hazel had a perfectly average intelligence, which meant she couldn't think about anything except in short bursts.
There were tears on Hazel's cheeks, but she'd forgotten for the moment what they were about.
(Vonnegut, "Harrison Bergeron," tnellen.com)
This shows how the handicap amendments work; a baseline of intelligence was chosen, likely as an average of the population, and then people were handicapped to lower them to that average. Hazel happens to be right on that average intelligence level. George is lowered to Hazel's average, but Hazel needs no lowering, and she can't be handicapped further, because then she would be inferior to the average.
Hazel has no handicaps because she is the standard for being perfect. The Handicapper General is forcing everyone to wear handicaps to refrain from hurting anyone’s feeling. However, in doing so the Handicapper General (Diana Moon Glampers) makes everyone miserable. Vonnegut is satirizing the idea of absolute equality between everyone in the story. No one can be equal because everyone is born differently. The author is also satirizing the idea that everyone should get praise or something in return for doing nothing. Kurt feels this is a stupid idea because he believes that in order to gain something; you must first do something to earn whatever you will be receiving. Satire is an author's way of criticizing something he/she feels is stupid. However, the criticism is done in a humorous way.