The government requires George, Harrison Bergeron's father, to wear a radio transmitter in his ear. Periodically, the government transmits a signal to George's earpiece and the earpieces of other citizens who are of above-average intelligence. Anyone who is smarter than Hazel, that is, who has an attention span no longer than "short bursts," receives a screeching signal every twenty seconds or so. The sound is so annoying and painful that it interrupts the thoughts of the intelligent people so that they aren't able to take "unfair advantage of their brains" and understand or discover things that their less intelligent counterparts can't figure out.
This serves to equalize the population so that "nobody was smarter than anybody else." Not only that, it keeps the intelligent members of society from having the mental space and energy to question the wisdom and/or morality of the decisions of the United States Handicapper General. Just as George begins to think about whether ballerinas should be handicapped, he gets the transmission in his ear, and he loses track of that idea.
Thankfully, nothing remotely resembling this level of totalitarian control of citizens using technology exists today. However, the demand for "fairness" that Vonnegut satirizes in the story was a reaction to trends that he observed in the US. Measures like affirmative action, which attempts to balance the deficit of minority populations in higher education, could be perceived to "inhibit" certain populations for the benefit of other. However, the key difference between Vonnegut's satire and Affirmative Action is that affirmative action seeks to address a problem that is due to systemic societal oppression, rather than an inherent lack of "talent," and that people are not being explicitly prohibited from exhibiting any exceptional abilities.
To take an example from reality, the government might also be thought to interfere with the free exercise of talent today by passing regulations that make it harder for inventors or businesspeople to implement their ideas in the marketplace. Biomedical devices, for instance, must go through a long and expensive approval process before they can be sold to the general public. This might be one way that the government is "holding back" talented people from exercising their talents (and profiting from these inventions). However, once again, the rationale for such regulations is not to level the playing field so that less talented citizens can compete—it is mostly to ensure the safety of the consumers of this product.
Vonnegut was also satirizing government bureaucracy and its seeming removal from reality, illustrated through a satirical situation that clearly demonstrates its absurdity. Vonnegut imagined an extreme scenario that would probably never occur, but it is effective as satire that points out how ridiculous valuing "equal outcomes" is (as opposed to creating "equal opportunity").