Saxony seems to have been located next to the german northwestern shore during roman times, yet when i look at a map today, it seems to be located a couple of hundred kilometers to the south east, right next to the czech border.
Was this a sudden move, or did the borders just gradually move around within the holy roman empire due to weird inheritances and politics? Or did something else happen?
The original Duchy of Saxony was located more or less where the modern German state of Lower Saxony is today, but over the centuries the ruling families acquired land and title in other parts of Germany, notably along the Elbe river around the city of Wittenberg. After the Saxon duke Henry the Lion was deposed by Barbarossa, the Duchy was split into a dozen or more smaller territories, and the ruling Ascanian dynasty was left with three non-contiguous territories.
In 1295/6, the three disconnected pieces of Saxony were legally partitioned, with two of them, Saxe-Wittenberg and Saxe-Lauenburg, both claiming the Saxon electoral dignity. In the election of 1314, the two lines of Saxon electors voted differently; the elector of Saxe-Lauenburg voted for Frederick the Fair while Saxe-Wittenberg voted for Louis the Bavarian. As a result, Louis granted the electoral dignity permanently to Saxe-Wittenberg, which became the Electorate of Saxony in 1356.
In 1422, the Ascanian line became extinct and the Electorate passed to Frederick IV, Margrave of Meissen, who also controlled Thuringia. The combined territory became known as Upper Saxony.
Upper Saxony itself would go through multiple territorial changes, but by the middle of the 16th century the Electorate of Saxony's borders were more or less the same as the modern state of Saxony, with the capital at Dresden.