In this story the world is dominated by - well, morons, because they have 'outbred' the intelligent. A tiny minority of intelligent people attempt to steer the 'morons', although all positions of authority seem to be taken by idiots.
...while you and your kind were being prudent and foresighted and not having children, the migrant workers, slum dwellers, and tenant farmers were shiftlessly and short-sightedly having children -- breeding, breeding. My God, how they bred! [...] Your intelligence was bred out. It is gone. Children that should have been born never were. The just-average, they'll-get-along majority took over the population. The average IQ now is forty-five.
In the end the protagonist introduces the beleaguered intelligentsia to the concept of 'genocide' and they set about slaughtering the morons en masse, by sending them into space. Not unlike the Golgafrinchans in the third ark. The story has a kind of twist ending, which you've probably already guessed.
There's a discussion about this story here. Some people think the story makes its case seriously, and it is despicable. Some people (as someone says in those comments, the Rand/Heinlein demographic) think Kornbluth was making a good point, a good prediction . Some people like this guy think the story is obviously a satire, or black humour, intended to make us question eugenics.
Whatever, the story is worth reading. Partly because it dramatises what it's like to live in a society which sometimes makes you feel alienated, where you feel like a beleaguered minority, where reading books makes you unusual. And partly because it does make you confront the unpleasant implications of that feeling.
Link to the discussion nicked from ninebelow.