Charles VI, the father of Maria Theresa, was the last of the direct male line of the Austrian Hapsburgs, who ruled the Austrian Empire. This caused a problem because according to Hapsburg law, only males could inherit the Hapsburg land. He attempted to solve this situation by the Pragmatic Sanction of 1713.
This in effect was a revision of the law that allowed his daughter to inherit the lands and thus the throne. Through long negotiations and diplomacy, he persuaded all the major powers of Europe including Prussia to agree to this international treaty.
In 1740, this sanction went into effect with the death of Charles VI. At first, it seemed that it would work, however, the Prussian ruler, Frederick the Great, came to the throne of power at the same time as Maria gained her inheritance.
Frederick was an ambitious ruler, who without declaring war had ordered his armies into Austrian Silesia less than two months after the death of Charles VI. This was the opening of the Silesian wars, which merged into the War of the Austrian Succession and the Seven Years' War.
France came to his aid. England and Spain were already at war with each other over Jenkins's Ear. The two wars merged, with Britain as Austria's ally.
An interesting side note to the whole matter was that three other monarchs had laid their claims to the Austrian Empire after Charles VI's death. The three monarchs were Charles Alpert, Elector of Bavaria; Philip V, King of Spain; and August III, King of Poland and Elector of Saxony.
The peace treaties restored the position of the Austrian crown to what it had been before the war. The powers accepted the Pragmatic Sanction, and Frederick the Great ratified the election of Maria Theresa's consort, Francis I of Lorraine, as Holy Roman emperor. Thus, the empire was returned to the new ruling house of Austria, the house of Hapsburg-Lorraine.
To understand and read further about this conflict, take a look at the following websites that cover this topic.
Modern Europe—Rise of Prussia
The Heritage History website gives you a general overview of this country and its beginnings. A good spot to start learning about nation-building. It is a good website for homeschoolers to use.
History of the War
From the Info Please website, read about this war and discover the major players and battles in Europe.
The Pragmatic Sanction
From the Catholic Encyclopedia website, read about this document that started the war over the Austrian Succession.