It is stated that George Bergeron is exceptionally intelligent, which means that he is not equal to the average citizen; being superior, he must be handicapped so he will not make anyone else feel inferior. His handicap is an audio speaker in his ear that generates loud, distracting sounds in response to his mental activity; the result is that he cannot think about anything for longer than half a minute or so without being distracted. The sounds are also always different, so he won't get used to any one sound.
"Who knows better than I do what normal is?" said Hazel.
"Right," said George. He began to think glimmeringly about his abnormal son who was now in jail, about Harrison, but a twenty-one-gun salute in his head stopped that.
(Vonnegut, "Harrison Bergeron," tnellen.com)
There are two main reasons to handicap George so drastically. First, as mentioned, he is not allowed to make anyone feel inferior with his intellect. Secondly, the government correctly assumes that anyone intelligent will resent their intrusion into private life, and eventually rebel. To keep people like George from using their intellect to their disadvantage, the government erodes his ability to think, neutralizing the danger.