You could read the whole story on wikipedia if you know what to search for. I've put good search terms in quotation marks. You're interested in the "War of Austrian Succession." I think it's sort of misleading to view it as a conflict between Prussia and Hungary.

Maria Theresa, as described in the "pragmatic sanction", was supposed to inherit the lands of her father, Emperor Karl IV, despite being a girl. But Karl Albrecht of Bavaria also wanted to be emperor, and made promises to a slew of powers to win their support for his candidacy: France, Saxony, Prussia, and Spain were all going to get new territories. See "Alliance of Nymphenburg." The result was a general struggle over who would inherit the Habsburg Lands, in other words, who would inherit the Austrian Empire. Thus, the war of Austrian succession.

Hungary had been a Habsburg possession under Karl IV, and the Hungarian aristocracy preferred Maria Theresa to Karl Albrecht. Maria Theresa swayed them with a notable speech: she showed them her young son and appealed to their chivalry.

King Friedrich II of Brandenburg-Prussia, better known as "Frederick the Great," was party to the alliance of Nymphenburg. He fought against Maria Theresa because if Karl Albrecht had become Emperor, Karl-Albrecht would have ceded Silesia to Friedrich.

Frederick II had long had his eye on expanding Prussian territory, but had always lacked the appropriate political climate to act. The death of the Austrian Emperor and the ascension of his daughter to the throne created the right environment and pretext needed for him to act. Thus his decision to invade Silesia, a resource rich province of Austria, in 1740. The two distinct factions quickly sized up with Austria, Britain, The Dutch Republic, Saxony (after switching sides), and at various points Russia. On the other side was France, Prussia, Spain, Saxony (before switching sides), Bavaria, and in late stages of the war Sweden.

The outcome of the war like most European wars at the time was to return to the relative status quo before war. Frederick got Silesia, Maria and her husband ascended to the throne, France returned much if not all of its hard fought and captured territory, and Spain got relatively nothing for her troubles as well. The larger affects on history are numerous. The Battle of Culloden ended any hope the Stuart's may have held of reclaiming the English throne. The war and Prussia's subsequent success were a coming out party of sorts, signaling the beginning of a military dominance and intimidation not broken until the Napoleonic wars. Austria and Prussia essentially became the two premier Germanic powers, both spending a considerable amount of time investing in a single unified German state with themselves at the head. France perhaps never recovered from this war and despite their impressive successes had little to show for it but blood and debt. It was in many ways the quintessential problem with European warfare at the time and was a harbinger of ugliness to come in the future laying down the seeds for future conflicts arising out of pride and need for self aggrandizement that was never satisfied by the very nature of the style of warfare being fought. It was a self perpetuating cycle of warfare that was exhausted only after 6 more decades of warfare.