The Scattering was a major historical event that occurred in the chaotic period following the death of Leto Atreides II, the God-Emperor. Leto's death saw the eventual breakdown of his empire, severe famine on many worlds, and the introduction of Ixian no-ships. It was all part of The Golden Path, as put forward by Leto, which was triggered by a perceived need to diversify the human race and allow it to evolve.
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Leto II's prescience allowed him to see into both the past and the future, and he believed that ten thousand years of rule by the Faufreluches had allowed the human race to become stagnant, and that drastic action on Leto's part was needed in order for the human race to survive.

As a result of this philosophy, during the reign of Leto II humanity was predominantly planet bound and ruled by an iron fist for more than 3500 years. This was in contrast to the relative freedom of expression and movement people enjoyed to a limited degree under the Faufreluches, the limits being predominantly the inherent control of feudal rule and the Spacing Guild monopoly on space travel. Indeed, Leto II exerted a level of control that was unprecedented in the Imperium, including power over the Guild and space travel, a feat that previous Emperors had been unable to accomplish. Upon Leto's death, the stalwart and long-established order of the Imperium disintegrated, as did control over freedoms and movement, and as a result, humanity rediscovered independence and nobilities on an unprecedented scale. This paved the way for humanity to "scatter" across the universe into the unknown and further evolution of the human race.

http://dune.wikia.com/wiki/Scattering