In Frank Herbert's Dune books, the Kwisatz Haderach was a foretold male individual or prophesied messiah with extraordinary abilities. Creating this man was a major goal of the Bene Geserit breeding program.
The name means "The shortening of the way". The Kwisatz Haderach would have abilities similar to a Bene Geserit Reverend Mother. The Reverent Mothers, after taking the spice, were able to look within and access ancestral memories, but only in the female line. Thus they tried to breed a man who would have access to both male and female lines. Because of this, he would also have many other abilities learned from his ancestors - in the Dune universe, these are considerable. He would also be able to see the future.
Reverend Mother Gaius Helen Mohaim: Thinks: Could he be the one? Maybe, but will he be ours to control?
Aloud: Do you know of the water of life? The bile from the new-born worms of Arrakis?
Paul Atreides: I have heard of it.
RM: It is very dangerous. The Bene Gesserit Sisterhood use it to see within. There is a place terrifying to us. To women. It is said, a man will come, the Kwisatz Haderach. He will go where we can not. Many men have tried.
Paul: They tried and failed?
RM: They tried and died.
- Exposition from the film Dune, the flawed but brilliant adaptation by David Lynch/Dino de Laurentiis of Frank Herbert's book.
Paul Atreides/ Muad'Dib was of course the Kwisatz Haderach. He became so by being the first man to drink the water of life and live through the resulting spice agony. He was not under Bene Geserit control, and indeed ended up controlling them. The Bene Geserit commanded Paul's Mother Jessica to bear only daughters to Duke Leto Atreides, but she disobeyed them out of love, and fulfilled the breeding program one generation earlier than expected. The daughter was to have been bred with a Harkonnen.
Paul's son, Leto II also had the abilities of the Kwisatz Haderach, and in fact deals with them better - instead of vanishing into the desert, he ruled for thousands of years as the God Emperor of Dune.