The name Saxon is supposed to have been based on the knife, the seax. (http://en.wikipedia.org/wiki/Saxons) The Saxons who invaded England, from the fifth century on, did not come from modern Saxony, although they were a Germanic tribe. They were were from the northwestern areas of modern Germany - Jutland and Schleswig-Holstein. (http://en.wikipedia.org/wiki/Saxons) according to the writings of Ptolemy.
The Saxon invasion took place at the time of the collapse of Roman authority across its empire. Angles, Jutes, Frisians and other tribes also invaded or migrated to Britain in the same era.
The cause for the mass migrations around Europe can be found in the movement of the Huns.in the fourth century. This nomadic people spread out from Mongolia in search of new pastures and booty. Their incredibly skilled horsemanship and mastery of the technology needed for fighting from horses (archery) enabled them to cover thousands of miles very rapidly and to strike without warning. The Mongol warriors attacked China, india, Iran and europe. Throughout the fourth and fifth centuries, the Huns, one group of Mongols attacked Europe, getting as far as Gaul and italy. The Hun adavance disintegrated after Attila the Hun's death in 453 AD but their actions had destabilised Western Europe, displacing many Germanic tribes, including the Saxons. These tribes were themselves compelled to move in search of land. It was largely the activities of the Ostrogoths that brought down Rome. In the power vacuum left by the collapse of the central authority of the Empire, the Germanic tribes took over the lands that the Romans had controlled.