The name given to the Hapsburg dominion from 1867 until its dissolution 1918. Also known as the "Dual Monarchy".
Hungary was always on the front line between Austria, the easternmost outpost of the Holy Roman Empire, and the Ottoman Empire. The boundary between Austria and Turkey shifted back and forth for centuries. Along with the constant misery of living in a battlefield, the nobility and eventually the people of Hungary enjoyed autonomy not seen elsewhere in the Empire except for the Germans in Austria proper.
By the 19th century, however, Austria ruled all of Hungary, and the Ottoman Empire had become the "Sick man of Europe". Immediately after the Congress of Vienna Austria had gained new territory and influence and a sound hold over Hungary. The failed revolutions of 1848 gave the Hapsburgs a chance to crack down on rights all over.
However, these same revolutions revealed cracks in Austria's ability to hold its polyglot empire together -- German-speaking Austrians were only 5 million out of an empire of 30 million.
It was in this atmosphere in 1866 that Prussian chancellor Otto von Bismarck decided to lead his country in an exercise in empire building, by goading the Austrian Empire into war. The whole goal of the Austro-Prussian War was to bind the smaller German states militarily with Prussia.
Prussia and its allies defeated the Austrians in a short, humiliating war with only one real battle. This war rendered the Hapsburgs unable to hold onto all of their territory -- a recenly-reunified Italy seized Venetia and Istria. What was worse (from the Emperor's perspective at least), the Empire's numerous Slavic peoples, and even the Hungarians, were agitating for more rights.
Rather than let his empire fly apart, the Emperor decided to cut its largest ethnic group in on the political pie. A new constitution, approved in December 1867, raised Hungary to the same political status as Austria. Formally, Hungary was raised to a Kingdom and the Hungarian parliament could pass laws only the Emperor could veto.
Although the constitution guaranteed equal rights for all its citizens on paper, it really didn't work that way. For instance, the right to vote was still tied to property. Not only that, it thwarted the national ambitions of the Czechs, Slovaks, Poles, Slovenes, and Croats under Hapsburg rule. The Emperor only made matters worse by annexing Bosnia-Herzegovina and making an enemy of Serbia which had wanted the territory for itself.
So, on the eve of World War I, the Dual Monarchy was almost as sick as the "sick man", Turkey, itself. Indeed, the poor performance of the Austrian army on the Eastern Front caused an allied German general to exclaim "We have shackled ourselves to a corpse!" Things were so bad that Germany had to take over the Austrian army to keep it from losing Bosnia-Herzegovina to Serbia.
After the end of the war, there was no question but that this golem of a state had to go. Czechoslovakia and Hungary were carved entirely out of Austria-Hungary, South Tyrol was given to Italy, Galicia was given back to Poland, Transylvania was given to Romania, and Dalmatia, Croatia, Bosnia-Herzegovnia and Slovenia were merged with Serbia and Montenegro to form the Kingdom of Yugoslavia.