After the Austro-Hungarian Compromise of 1867 the lands of the Austrian half of the Empire (Lower Austria, Upper Austria, Styria, Carinthia, Carniola, the Austrian Littoral, Salzburg, Tyrol and Vorarlberg, Bohemia, Moravia, Silesia, Galicia and Lodomeria, Bukovina and Dalmatia) were referred to as the ‘Kingdoms and Lands represented in the Imperial Council’ or Cisleithania for short.
Transleithania referred to the lands of the Hungarian Crown (the historical Kingdom of Hungary together with Croatia and Slavonia and the free city of Fiume).
Literally these unofficial names meant ‘the lands on this side of’ or ‘the lands beyond’ the River Leitha, which marked the historical border between Austria and Hungary.